There are competing explanations for why the Yamato and Musashi did not play a greater role in Japanese naval operations earlier in the war. One explanation (as /u/TheOtherDrunkenOtter guessed) is that the Yamato and Musashi both required large amounts of fuel. The Japanese had to constantly monitor their oil stores throughout the war, and using the Yamato-class battleships would have been a costly use of oil. Another explanation is that the Yamato and Musashi were being held in reserve for a decisive naval battle in line with Japanese naval doctrine at the time. The Japanese navy was reluctant to commit the battleships to operations that were not seen as central to the war effort or to risk them in battles that would not tilt the balance of the war anyway. A third theory is that Japanese naval commanders understood the new battleships were poorly suited for the naval battles of 1942 and 1943. Despite their fearsome reputation, they would have been vulnerable to aircraft at any point in the war. There were only two instances of battleship-on-battleship combat in the Pacific; one during the Guadalcanal campaign in late 1942 and one at the Battle of Surigao Strait during Leyte Gulf.

Introduction

For those unfamiliar, the two Yamato-class battleships are still the largest warships ever put to sea other than American supercarriers that didn't sail until after World War II. They wielded nine guns of 18.1 inches, exceeding the 16-inch main guns aboard the largest American battleships ever built. The Musashi, the second ship in the class, was not commissioned until August 1942 (which is one reason why she did not participate in battles earlier in the war). She was sunk by American carrier aircraft at the Battle of the Sibuyan Sea in October 1944 as part of the larger Battle of Leyte Gulf. Yamato joined the Japanese fleet in December 1941, shortly after Pearl Harbor. She survived Leyte Gulf and was sunk by American carrier planes in a futile effort to beach herself on Okinawa in 1945. By the time Musashi and Yamato were sunk, the Japanese fleet was clearly outmatched by the American navy and the battleships had no chance of playing a significant role in the war. Both Yamato and Musashi served as flagships for the Japanese fleet at different points during the war. Both were also sometimes referred to derisively as "Hotel Yamato" or "Hotel Musashi" because of their relatively spacious accommodations and their stationary status. While much of the Japanese fleet was worked to the bone with constant operations, the Yamato and Musashi spent a disproportionate amount of time anchored at the base at Truk or in Japanese ports.

Fuel Consumption

The Yamatos were thirsty ships indeed. Each had a fuel tank that held 6,500 tons of fuel – about the same weight as a Japanese light cruiser during the war. Capital ships were often outfitted with large fuel tanks to provide refueling to their escorts, but the battleships did burn tremendous amounts of fuel when operating under battle conditions. Yamato burned 62.7 tons of fuel per hour when undergoing speed trials; operating other systems aboard necessary for battle would have pushed that figure even higher. Combined Fleet, a website run by Shattered Sword co-authors Jonathan Parshall and Anthony Tully, includes a lengthy examination of the fuel situation in late 1942 when Yamato and Musashi could have been committed to an engagement in Guadalcanal. Their estimate is that for Yamato and Musashi (plus the necessary escorts) to make a single bombardment of Henderson Field, it would have cost the Japanese Navy more than 15,000 tons of fuel at a time when the entire Japanese navy could only expend about 305,000 tons of fuel per month.

An argument in favor of such a mission – even with the benefit of hindsight – would point out that the Japanese successfully sent a force that included two Kongo-class battleships to bombard Guadalcanal on the night of October 13-14, 1942. The bombardment is remembered by Americans on Guadalcanal as one of the lowest points of the campaign. Dozens of aircraft were destroyed at Henderson Field, the airstrip was damaged, and facilities took a beating. Soldiers and Marines on Guadalcanal were no strangers to naval bombardment, but the 14-inch shells from Kongo and Haruna were more destructive than anything they had experienced before. The Americans were able to resume some flight operations at Henderson Field the next day and received more aircraft, but not until after the Japanese had landed reinforcements elsewhere on the island thanks in part to the battleships.

Sending Yamato and/or Musashi on a similar mission might have done more damage, but Kongo and Haruna were more fuel efficient than the bigger battleships. The Kongos were originally built as battlecruisers, thus carrying much less armor and weighing much less than the Yamatos. There are also valid questions about whether the Yamatos could have done enough damage to alter the outcome of the campaign. Holes in austere runways (like Henderson Field) can be filled in and patched over in short order no matter their size. The Yamatos might have done more damage to facilities or destroyed more aircraft, but wouldn’t have prevented the Americans from flying more planes in later. Some have also questioned whether the Yamatos even had enough ammunition for shore bombardment, rather than shells meant for naval combat. The Japanese war economy was so strained that even producing extra munitions might have been difficult.

Two other Kongo-class battleships returned to Guadalcanal in November 1942; Hiei was crippled after a brutal night engagement with American cruisers and destroyers, then sunk by aircraft the next day. Kirishima was sunk two days later following another night engagement with the American battleships Washington and South Dakota. The presence of a Yamato here might have turned the battle into a Japanese victory (and it would have delivered a clash of some of the war’s best battleships), but even sinking Washington and South Dakota would not have changed the overall situation at Guadalcanal. Control of Henderson Field gave the Americans air superiority during the day, and the Japanese could not turn the tide of the campaign without a sustained presence around the island. That was never possible because of their inability to win control of the skies.

Decisive Battle

That segues into the second explanation. The Japanese may have understood that no single naval engagement around Guadalcanal could be decisive, and thus withheld their prized battleships. Japanese pre-war naval doctrine was focused around a decisive battle, called kantai kessen. The basic idea was to engage in a large-scale fleet engagement that would result in a clear victory like the one the Japanese had achieved at Tsushima in the Russo-Japanese War. The Japanese navy was constrained by interwar naval treaties that limited the size of its fleet compared to its American rivals. With this in mind, the IJN sought to develop qualitative advantages over the Americans. Its destroyers and cruisers were armed with the Type 93 torpedo, capable of sinking large American warships. Japanese crews were trained to fight in nighttime engagements. Japanese aircraft were expected to fly from aircraft carriers and island bases across the Pacific to whittle away the American fleet as it sailed thousands of miles away. By the time the American fleet arrived for battle with the Japanese, the superior ships and men of the Japanese navy would be able to win a clear victory. Japan originally planned for five Yamato-class battleships. A battle line of five Yamatos would have been the backbone of the Japanese surface fleet in this engagement. The Japanese never sought a war of attrition and continued to look for chances to win a decisive battle. The fighting in the Solomon Islands in 1942-43 was classic attrition warfare, and there were few good opportunities to use the Yamatos.

It’s worth noting that Yamato did sortie with the Japanese fleet in the Midway operation, which was conceived of as a chance to defeat the Americans in a decisive battle (Musashi was not yet complete in June 1942). Yamato and Musashi both left port to participate in the Battle of the Philippine Sea in 1944, which was also envisioned as a chance to engage the American fleet on equal terms. The battleships participated in some other operations that were not considered decisive battles, but they were not wholly inactive until 1944. Yamato also took a torpedo hit from an American submarine in December 1943; Musashi was hit by an American submarine in March 1944. These attacks required time in port for repair.

In some sense Yamato was committed previously. She sortied along with the rest of Battleship Division 1 as the core of the the Japanese Main Body for Operation MI. In the original plan envisioned by Admiral Yamamoto, Yamato and the Main Body would be present to deal with a follow on American surface fleet. While the outcome of the carrier engagement at the Battle of Midway (and the lack of any American battlefleet to engage) would prevent the Yamato from carrying out its mission, she was absolutely committed to Operation MI.

Similarly, for most of 1943, the Imperial Japanese Navy was working feverishly to reconstruct its carrier air arm. The battles of 1942 had taught the IJN that any future engagement would be heavily decided by carrier aircraft, and it had revised its doctrine to emphasise carrier operations above the battleships. While previous Japanese naval doctrine had been all about the decisive battle between battleships, the new doctrine had the battleships positioned as a vanguard force, where they could scout for and provide a defensive buffer against incoming attacks. However, the carrier battles of 1942 and the Solomons Islands campaign had bled Japanese naval air white. The elite carrier aircrews from the surviving fleet carriers Shōkaku and Zuikaku had been reassigned to shore duty, where they too were ground down. Similarly, the Japanese recognised that even were they to aim for a major surface engagement, their battleships would not be effective unless they could maintain air superiority over the area of battle. Thus, for 1943, the Japanese focus was on rebuilding its air strength, allowing time for new aircrews to be trained and deployed. With the American advance into the Central Pacific underway, the Japanese recognised that their limited naval assets would have to be husbanded to challenge the American fleet. The outlying islands in the Gilbert and Marshall Islands served their role by slowing down American forces, buying the Japanese time. The Japanese wanted to hold onto their available naval forces until there was an opportunity for them to deal a decisive blow to the American fleet, and so the fleet was held back for the campaigns of 1943. Ideally, the Americans would have taken more serious losses taking these islands, and have been delayed longer, but--as the case may be--in mid-1944, the Americans were ready to threaten the islands of Japan's inner defensive ring, and so the Japanese would have to challenge the American fleet. Regardless, 1943 was to be a quiet year for the IJN, biding its time as it prepared to respond to later American offensives, as it would do with Operation A-Go and the Battle of the Philippine Sea. While the battleships were available, to deploy them without appropriate air support would have been nearly suicidal, and it was only desperation that led to exactly such a committal at Leyte Gulf.

The questions thus becomes: why did the Japanese not commit their battleships--including Yamato and Musashi--to the Solomon Islands campaign, particularly the naval battles of Guadalcanal? After all, had Yamato and her 18" guns been present at some of the naval engagements there, the outcome could have been very different. There are a number of potential factors at work here. /u/Myrmidon99 has delved into this question a great deal, and I think resolves it very well. There were questions of whether the Yamato class ships would have even been useful, whether the Japanese recognised the importance of the Solomon Islands Campaign or were trying to preserve their battleline for future engagements, or if the fuel costs of deploying the battleships were simply to great for the IJN to sustain given the limitations on the fuel supply. I will say that relying on estimates of Japanese refined fuel capacity may be a little misleading, as the Japanese had shown that they were more than willing to fuel their ships with raw crude straight from the pumping stations in the Dutch East Indies. While a ship running on crude is undoubtedly going to be less efficient than a ship running on refined fuel oil, it does provide a bit of a gap for a sortie.

So, with that out of the way, we have a few answers to your question: 1) the Yamato was committed to "the Decisive Battle" of Operation MI in June 1942, but was not committed to the other carrier battles of 1942 or the Solomons Campaign for a variety of potential reasons, including a desire to maintain them as a reserve, concerns about fuel consumption, etc.; 2) during the American campaigns of 1943, the Japanese were heavily focused on rebuilding their naval air arm following the defeats of 1942, and so the Navy was on a defensive stance while the Americans pushed their way through Japan's outer defenses. By the time the Americans began to threaten the inner defensive chain at Saipan in the Marianas, the Japanese committed their fleet in an effort to prevent first the fall of the Marianas and second the fall of the Philippines in what they hoped would be other "decisive battles". Fittingly, the Yamato class ships were committed to both of these operations.