American escort tactics can roughly be broken down into two "eras" in the European Theater (ETO) during WWII: pre-Doolittle and post-Doolittle.

Pre-Doolittle From 1942 to the end of 1943, American commanders operated under the premise that the bombers could fend for themselves. They believed that the heavily-armed bombers could make it to the target and back with minimal fighter escort, if any at all. They really bought into the idea that they were sending "flying fortresses" over Europe. It helped somewhat that they initially sent them to easier targets. These targets were in occupied territory, like France, and were not as heavily defended by either fighters or flak. As numbers built up, however, it was a given that the commanders would have to really put their theories to the test by sending the bombers into Germany, and eventually into deep Germany.

As they did this, they soon realized that the bombers could not, in fact, fend for themselves. So they tried different formations in an effort to maximize the coverage of the defensive guns on the bombers. Eventually they settled on the "box formation." This formation would pack the bombers together tight in a way that each bomber could cover each other.

Still, though, the box formation was not enough, and losses continued to mount. So they increased their attempts at fighter cover. Eventually, they were sending the bombers out on virtually every mission with fighter protection. The problem, though, was the range that fighters had; or more precisely, the range that the fighters did not have.

Early in the war, the Allied powers in Europe had essentially three different types of fighters to choose from for escort missions; they could choose the American P-47, the American P-38, or the British Spitfire. These fighters, even with external drop tanks, could only make it partway over the continent on their escort missions. Mission that saw the bombers go deep into Germany (the Schweinfurt-Regensburg missions, for example) would have the bombers completely alone for period of 4 hours or more. That's a long time on your own when each defensive gun only carries enough ammunition for roughly 60 seconds of continuous firing.

But to get to your question, when the fighters were there, their orders were essentially to stay with the bombers. Essentially, their mission was to "shoo" the Germans away from the bomber stream. Shooting down the Germans was supposed to be secondary to keeping the bombers alive.

To do this, the Americans (or British, if they were flying escort that day) would fly a weaving pattern above the bomber stream. This allowed them to keep their speed up. Remember, in a dogfight, speed = life. The fighters were not flying formation with the bombers. All of those movies where the fighters tuck into the bomber formation are bullshit.

The fighters are flying a thousand or more feet above the bombers. As the bombers are flying ----------- that way, the fighters are flying VVVVVVVVV. This way, it is easier for them to scan the sky for the Luftwaffe. And when they do spot the Germans, they have a height advantage (or they may have a height advantage. The Germans loved to dive down on the bombers, if possible).

Even though their orders were to stay with the bombers, many of the fighters would go off and chase the Germans. This led to a wild scattering of dogfights with little real coordination and organization.

The Germans realized this, and soon they began sending in fighters to lure the escorts away, and once the escorts were away, then they sent in more fighters to focus on the bombers.

Post-Doolittle At the start of 1944, the American commanders put Jimmy Doolittle in charge of the 8th Air Force in England. He immediately changed their tactics. Knowing that the invasion of Europe of was rapidly approaching, he had to eliminate the Luftwaffe. So the main focus of the American bombing campaign shifted from a general "destroy their ability to wage war" focus to a focus on "destroy the Luftwaffe." To do this, they targeted airfields; aircraft factories; the oil refineries that gave the Luftwaffe their fuel; etc.

Additionally, he ordered the fighters to target the fighters first. No more of the protect the bombers mantra; the fighters were there to destroy the Luftwaffe, plain and simple. The bombers would be the reason to draw the Luftwaffe into the skies; the fighters would be there to meet them. If the Germans didn't want to fight, they would be destroyed on the ground via bombing or strafing.

It helped tremendously that around this time the Americans started to take delivery of large numbers of P-51 Mustang fighters. These fighters could fly every mile of the mission that the bombers could and stay with them all the way to Berlin. The bombers would no longer be without fighter cover over Germany.

So, now a mission for a P-51 pilot would consist of his formation from his group flying to a rendezvous point. There they would meet the bomber stream, and they would escort it for a certain leg of the mission.

(So even though the P-51 could fly to Berlin, it couldn't be expected to fight the entire way there and back. So on a longer mission, the bombers would be escorted in shifts. There would be, say, 5 groups of fighters that would tag-team in and out along the way. Group 1 escorts them from the coast to 100 miles inland and breaks off to go home; group 2 escorts from 100 miles inland to 200 miles inland and then goes home; etc.)

Once rendezvoused with the bombers, the fighters, depending which part of the bomber stream they were assigned to, would take up that familiar zig-zag pattern, scanning the skies for Germans.

Other groups, however, were given permission to roam ahead of the bomber stream and attack the Germans as they were forming up. The Germans were accustomed to doing the attacking, not being attacked. Now they were being hunted at their airfields during takeoff; they were being stalked as they grouped together into formations; they were jumped as they flew to their own rendezvous points. Nowhere was safe for a German pilot.

If the Mustang pilots hadn't been one of the groups allowed to roam ahead, or if they just hadn't found anything, then when they returned home, they would attack targets of opportunity. They would strafe anything that looked military in nature. Pilots would even strafe cows in open pastures so that they couldn't be slaughtered and eaten by hungry German troops. Virtually anything that was of potential military significance was fair game.

By the time D-Day came around, the Germans were able to put a mere 2 planes over the Normandy beaches in response.

Let me know if I didn't respond to all of your questions or if you have any others. I really love this topic, and don't mind discussing it at length.

By this time of the air war, the Luftwaffe is severely depleted in terms of men and available machines which made successful interception of the USAAF bomber forces difficult. Assuming that the Luftwaffe got up, it is likely that they would have tried to intercept bomber formations either head on, or from above. Both of these approaches gave advantages to the attacker: Coming from the front severely reduced the ability of the bomber to defend itself, as frontal defences were severely lacking until the B17-G model fortress was introduced (it had a chin turret to help in frontal defences. Until then, frontal defences on B-17E/Fs were makeshift). On the other had, having the height advantage meant that the Luftwaffe could pick their targets and attack with the advantage of coming out of the sun, where it is difficult to see.

In terms of tactics, the Luftwaffe attempted mass attacks by large numbers of fighters and smaller attacks. Generally, these attacks weren't very successful and became less so as the war went on, as the Luftwaffe didn't have the men and materials that the allies had, which meant that attrition would wind up decimating the Luftwaffe and its' effectiveness. In an attempt to neutralise the threat of the long-range escort fighters, the Luftwaffe did try to "intercept' bomber formations in the English Channel. -Not so much to shoot down bombers, but more to force the escorting fighters to dump their drop tanks (which were still mostly full) and increase the time that the bombers would be without an escort and vulnerable.

From the USAAF perspective, Fighter escorts were an important piece of the air war puzzle, and they provided overlapping escorts that were proportional to the raid and objectives. The USAAF trialled various tactics, including flying both with and above the bombers. -I haven't seen enough to decisively say whether one tactic was preferred over the other, although I suspect that escorting fighters generally hovered above the bombers.

In terms of how an engagement would pan out, the Luftwaffe focussed almost exclusively on the bombers rather than the fighters, while the USAAF escorts would hunt in pairs (adapted form the Luftwaffe) to intercept the German fighters before they could engage the bombers. The Luftwaffe preferred to attack head on to the bombers, as the front of the B-16E/F B-17E/F wasn't well armed (the introduction of the B-17G changed this, with the introduction of a chin turret), although they still tried to gain the height advantage (one of the fundamentals of dogfighting).

So, from a P-51 pilot's perspective, you would probably have the height advantage over any Luftwaffe aircraft coming in to attack, plus the bonus that the Luftwaffe pilot was probably focussed on the bombers rather than you, making your job easier. Add in the attrition of experienced Luftwaffe pilots and your job would get easier and easier as 1944 crept into 1945.

Finally, after you had performed your duties and had been relieved by another escorting force, in 1944-45, you would have been under orders to return to England at low altitude, along a flight path "conveniently" close to known (and suspected) Luftwaffe aerodromes (and supply routes), with freedom to attack basically anything that moved... Thus giving escort fighters a second role focussed on destroying the Luftwaffe on the ground as well as in the air.

-Please accept my apologies, as I am not an expert on the daylight operations during the European Air War and I have probably missed a whole heap of stuff.

EDIT: Typo