Expanded from an earlier answer of mine

On paper, the Battle of Samar was highly asymmetrical. Outside of airpower, the IJN under Kurita did enjoy a massive advantage over Taffy 3. But looks are deceiving and the USN naval force had latent strengths that capitalized on the weaknesses of the IJN force.

For one thing, the lack of Japanese airpower was a massive advantage in the USN's favor. The escort carriers' planes were able to considerably disrupt the IJN's ability to form their fleet up into a coherent battle formation. The original Sho plans had called for considerable land-based air support, but Halsey's earlier carrier raids on Taiwan had caused a premature deployment of Japanese airpower. Whatever was left to the Japanese was considerably denuded and poorly coordinated. IJN surface units also possessed vulnerabilities. The expansion of the ships' AA added yet more ammunition which could be set ablaze. The IJN's heavy cruisers had proven to be formidable combatants in the Solomons, but they also had something of a glass jaw; a well-placed torpedo hit could severely damage or sink them. The IJN's use of evasive maneuvers to deal with aircraft attacks compounded some of these vulnerabilities. The heavy units could find themselves unsupported and thus vulnerable to a swarm attack despite their beefed up AA armament.

The actions of Kurita at Samar are still somewhat controversial among naval historians. Kurita in theory should have acted with daring given that the Sho plan called for a fight to the death, but he vacillated throughout the engagement. On a more tactical level, there is the question of why did Yamato and Nagato turn northwards at ca. 0755 which pulled the ship away from Taffy 3 and the carriers when the two battleships were relatively undamaged. Second, there is the Kurita's overall withdrawal for the IJN forces at 0920 away from the American escort carriers and transports. Both decisions by Kurita earned him a degree of opprobrium at the time and in the postwar period with one common metaphor employed casting Kurita as Hamlet unable to make a decision until after the die had been cast.

Of the two decisions, the Yamato turn is the more explicable. Lookouts had sighted torpedoes from an earlier torpedo attack and Kurita's battleships faced two choices to "fan the torpedoes", a turn to port (north) or starboard (south). The starboard turn would have kept the fleet into contact with Taffy 3 but posed two disadvantages. Firstly, it would have been steaming into the torpedo line, risking a hit. Second, it meant that both battleships were in serious danger of colliding with the battleship Haruna, which had been steaming in a line parallel to Kurita's division. This particular aspect of the division's decision is one that only very recently become apparent. Older historiography on Samar such as Morrison tended to place Haruna in a different location than more recent work like Robert Lundgren or John Prados which triangulates the battleline more closely using surviving Japanese and American accounts (and note, this still is reasonable conjecture, but still a hypothesis). The officers in charge of the ships' maneuvering instinctively chose the course that minimized damage, with the result that the two most powerful surface units at Samar were now seven miles out of position and its commander lacked even more situational awareness.

This uncertainty shines some light onto Kurita's second turn away from battle. When the US Strategic Bombing Survey (USSBS) interviewed some of the surviving Japanese naval officers, they gave some inkling that they knew after the battle that the opposing naval force was much smaller than they first thought at the start of the engagement. USSBS NO. 170 The Battle off Samar's interrogation of Commander Otani Tonosuke, Operations Officer on the Staff of CinC Second Fleet has a very instructive portion on this very issue and how Japan's lack of air cover contributed to the fog of war:

Q. What type of carriers did you believe they were?

A. We gave that question much consideration, but never fully made up our minds. We found ourselves perplexed by your carriers because they did not correspond to their photographs, and first we thought that they were regular carriers; but after the battle, we decided that they were auxiliary or converted carriers. Also we received word from the tops that there was another formation, and at that time we wondered if we were not confronted by 12 or 13 carriers in all; but this was not ascertained on the bridge.

Q. Was there any attempt to engage in battle with the second group?

A. First, we would encounter the first group, and then take on the second.

Q. What damage did you inflict upon the first group you engaged?

A. One carrier sunk, one light cruiser, one heavy cruiser and one destroyer. There was some confusion between the high gunnery control platform and the bridge. There may have been a repeat report which was understood as two carriers sunk; the bridge concluded that one carrier was sunk. Again from later reports which may have contained duplication, we concluded that we had sunk four carriers, two or three cruisers and two or three destroyers. That was the total result of the day. I now think this is rather accurate, and from a report of search planes at about 1100, we received information that one battleship was severely damaged and dead in the water.

As Commander Otani's interrogation made clear, the IJN's attempt to ascertain the reality of the combat situation was made difficult by the reliance upon visual sightings from surface ships and the constant Allied air attacks on Kurita's fleet. Kurita's USSBS interview likewise suggested that visual surface sightings were inadequate to give the IJN admiral a proper estimate of the situation:

Q. What type of aircraft carriers were the American carriers present? Were they the ESSEX or ENTERPRISE class? Did you recognize them?

A. I don't remember. Starboard bridge structure was all I could tell. There wasn't enough visibility nor adequate reports from the scouting planes.

Although he was not available for a USSBS interview because of his foolhardy Kamikaze mission. Admiral Ugaki Matome's diary entries for the Leyte battles also notes that Allied air attacks and poor Japanese reconnaissance doomed Japan's efforts to throw back the Leyte invasion. Although Ukagi's diary took Kurita to task for confusing orders, he placed a good deal of blame for Japan's defeat on the inability of the Philippine's airbases to provide the surface fleet any form of cover or information. His 24 October entry noted that:

Unless we get enough cooperation from our base air forces, we can do nothing about [concentrated American air attacks], and all of our fighting strength will be reduced to nothing at the end. In such case we should perish by fighting an air battle, hoping it to be a decisive one.

Once the gravity of the defeat off of Samar sank in, Ugaki's 25 October entry pinned responsibility for failure "in some respect to [the operation's] planning, [but] mostly to the extreme inactivity of the base air forces. Probably hindered by bad weather." One of the themes of Ugaki's remaining entries for October and November was lambasting Japan's lackluster efforts to produce as many aircraft as possible to turn back the Allied tide.

Although Kurita asserted in his interview that he did not expect air cover from land-based aircraft, Ugaki's diary entry indicates that at least some IJN officers expected an effort to be made by land-based planes. Otani placed a great deal of onus on the Sho operation's failure to poor coordination between Kurita and Japanese air assets:

Q. Where do you think this whole operation broke down? Why did it fail?

A. I feel that from the very beginning that the cooperation between the Task Force (OZAWA) and the Surface Force (KURITA) and the land-based Air Force was bad from the beginning.

Q. What do you feel caused this poor coordination?

A. Coordination between the Surface Force and the (carrier) Task Force was almost impossible due to the restrictions on communication and the need for radio silence; therefore, the plans for cooperation were not carried out. This lack of information from OZAWA was one of the main factors in the failure of the operation, but perhaps the biggest factor was the lack of protection from our land-based air against your (carrier) Task Force. I feel also that the original plan was too complex and inflexible to work properly.

PART I

I want to add to the terrific answer of /u/kieslowskifan and go up a few thousand feet, both literally and strategically.

Here was the basic problem: Sho-Go 1 is flawed from the start when the orders are issued on October 18th. The schedule from the Japanese side assumes that they've got a few days; air power gets redirected to Leyte on October 21st, air attacks are scheduled to start on October 23rd and 24th, and then the big naval battle is supposed to take place on the 25th.

But the Americans aren't working on the Japanese timetable. The landing begins on October 20th, when MacArthur's divinity comes into question as there's now photographic evidence he doesn't walk on water as he lands a few miles away on the northern part of Leyte - a few miles southeast of that island's provincial capital of Tacloban, which gets captured the following day. Over the next few days, his Sixth Army does its job quite well; there are a number of beachheads firmly established further southward along the east coast of Leyte to the point where MacArthur duplicates his wading several times as he visits them. By the 24th, he and his X and XIV corps commanders are now comfortable enough with the progress to move their headquarters from ship to shore, helped by the fact that the Japanese have made a massive mistake in thinking the Americans are only landing two divisions rather than a force of 200,000.

What does this mean for Sho? If your goal is to crush the landing force, you're too late; they and most of their supplies are already ashore; by the time Kurita arrives there are only maybe 30 out of several hundred transports that haven't offloaded yet - which, by the way, Kurita has a rough estimate of those numbers from a scout plane. Now a few days earlier, when troops and supplies are still embarked, they indeed are vulnerable to every single ship of Kurita's Central Force; sending his destroyers in to sink loaded troop ships stuck at anchorage off shore and unable to maneuver would have been catastrophic. But what years of American landings from Guadalcanal to Normandy have also proven is that while terrifying, the main effect of heavy caliber battleship gunnery once boots aren't wet anymore (to use the terminology of an old Marine I knew who'd fought in some of those very battles) is to force their targets to hunker down. That might slow down their advance a little bit, but overall it does the Japanese very little good strategically since a few days in Sixth Army has already captured most of the northeast of Leyte Island. This is not ideal if your goal is to push the Americans into the sea, but since nobody on the Japanese side is really making an effort to share information, this doesn't get fully relayed even in the Japanese Army, let alone to the Navy.

To give you an idea of what that kind of control on land means 96 hours later, before the massive naval battles that begin the night of the 24th, the Japanese Air Force launches a 200 plane strike during the day against American positions on Leyte. Army Air Force land based defenders are already robust enough so that they claim to shoot down a third of them outright. This is not what the Japanese Navy is counting on for air support.

So come midnight, thanks to Halsey's incompetence, Kurita completes his first objective: getting through San Bernardino Strait between southern Luzon and northern Samar unseen and untouched. He then steams east for the 70 miles of the northern coast of Samar and turns southeast for about another 100 miles - remember, Samar Island is a pretty big place with only its southern coast forming the northern side of Leyte Gulf. Then around 0645 he finally runs into American ships.

I'm not going to go into the battle on the water since the important part of the analysis is covered well above (and you've clearly read about it), but the air component of the battle is very much worth emphasizing since it often gets lost in the valor of the DDs and the DEs. All in, the 18 CVE jeep carriers of the three Taffys under Thomas Sprague's overall command - I like the the bluejacket term of "Combustible, Vulnerable, Expendable" used to describe them - have a pretty capable air component of 235 fighters and 143 torpedo bombers, which is roughly the equivalent of a fleet carrier group. They're spread out in about 20 mile intervals north to south, with Ziggy Sprague's (no relation to Thomas, although they were in the same Academy class) Taffy 3 taking the brunt of the attack. If Kurita had stuck around to finish them off, Taffy 2 under Felix Stump was next up.

But while that distance meant the other Taffys couldn't initially engage on the water - Taffy 1 under the direct command of Thomas Sprague was give or take 2 hours away at the flank speed of the jeep carriers - this wasn't a problem for the air wings. Taffy 1 was a little slow to respond as its planes were participating in the mop up of the southern Sho-Go force, but Taffy 2 had enough time to prepare a ship target loadout rather than land, and Taffy 3 went so far as to scramble everything they had, sometimes putting them in the air with just small caliber ammunition.

The other aspect to this was that nobody on the Japanese side knew they were fighting jeep carriers since their surface fleet had never done so before. In general, most of the IJN command assumed that these were instead Independence class light carriers, which had all sorts of implications for strategy. It meant that the wrong type of shells were used - choosing armor piercing shells meant they just poked holes through the thin CVE hulls, which probably would have been sunk with a single explosive charge - and given the light carriers could make a bit over 30 knots much like their 33+ knot bigger brother fleet carriers, IJN maneuvering was based on the belief that they had to close fast and maintain contact because at flank speed the carriers could simply slip over the horizon if they were given the option. Several hours of high speed approaches blew through an irreplaceable amount of fuel and time, especially since in reality the jeeps could barely get close to 20 knots and could have been easily dispatched if the IJN had a better idea of what they were fighting and adopted more appropriate tactics.

This also meant that from the Japanese perspective, they mistakenly thought they not only were fighting targets that were worth delaying their strike on the landing force and (arguably) sacrificing their own ships for, but also created the expectation for the entire staff that there was going to be substantial retaliation in the air - which in the couple hours of the attack on Taffy 3 had moved from initially annoying to somewhat problematic by the time Kurita turned around - given their previous experiences with American air power. In fact, many of the staff did not learn until after the war that their targets that day had been jeep carriers.