In the air, the Cactus Air Force was tying out new tactics to combat the agile Japanese Zero. "Cactus Air Force" is a nickname for the pilots of Henderson Field on Guadalcanal--codenamed Cactus. These pilots used a mix of aircraft, most notably the Grumman F4F Wildcats (there were some P-39's as well, and some dive bombers too). The Wildcat was heavily armed, heavily armored, and heavy overall compared to the Zero. If a Wildcat pilot tried to turn with a Zero in a dogfight, he would quickly end up with the agile Zero behind him. So, a naval aviator named Thatch came up with a defensive maneuvering scheme that came to be known as the Thatch Weave. This allowed pairs of Wildcats to keep their wingman covered from attack from behind. The linked wikipedia page has a good illustration of the tactic. Offensive tactics revolved around diving attacks or head-on passes, where the armament and armor of the Wildcat would make it the victor in most slugging matches.

At sea, there was a curious occurrence in warfare. Control of the area around Guadalcanal generally changed hands every twelve hours. During the day, the US Navy was able to largely command the waves--especially as Henderson Field became more established. At night, the Japanese expertise and experience at night fighting meant that they could exert control over the area. There were so many ships of both sides sunk in the area that it gained the nickname "Ironbottom Sound." The clashes gave US naval forces valuable but costly lessons that were applied in the later island hopping campaigns.

On land, the Japanese committed troops piecemeal to various assaults on the Marines. Again, the campaign was costly for the Americans and there were several times where the enemy nearly broke through. However, the Marines gained valuable tactical, logistical, and other lessons that applied to warfare in the theater. I don't know of any tactical breakthroughs that were made, instead there were refinements to existing ideas. Coordination between infantry and mortars/artillery was improved. Close air support was practiced (especially with the aforementioned P-39's and dive bombers). Officers and men gained experience in how the Japanese liked to fight as well as what was effective against them.

Guadalcanal: The Definitive Account of the Landmark Battle by Richard B. Frank is an outstanding account of the battle. Robert Leckie's Challenge for the Pacific: Guadalcanal: The Turning Point of the War is also good if a bit shorter. However, Leckie was an infantryman in the actual battle, so his insights are incredible. They are more intimately described in his memior: Helmet for my Pillow.

Not directly related to your question OP, but an excellent book that describes the changes made in the British Army's tactics/strategy etc etc in Burma against the Japanese is:

Slim, Master of War: Burma and the Birth of Modern Warfare.

(General Bill Slim, IMHO one of the most overlooked commanders of all Military Commanders of WWII)

(replying as this might have, at least some, relevance to your inquiries)

I wrote my undergrad thesis on a directly related topic. It is more about learning how to fight in the pacific in general, but deals with Guadalcanal.

Here's a link to a sanitized version of it on google docs, or you can contact me directly for a pdf link to the submitted version.

What it boiled down to was reworking significant portions of combat doctrine. Combined arms warfare, which was born in the later stages of WW1 and was on full display by 1939, didn't really work in the dense jungles of the Pacific. Small unit tactics were of increased importance, as large unit maneuvers were difficult to execute.

You know how you always hear about how armies are constantly training for the last war? That is relatively accurate, but it's not as bad as it would seem because usually there will be a great deal of similarity from war to war. Sure, the technology changed between the Napoleonic Wars and WW1, but they were still fighting over familiar land, and were simply adapting existing tactics to emergent technology.

In the Pacific, American (and to a far lesser extent British and ANZAC) had to rethink the way they would fight the war. It wasn't simply fighting the same war with new weapons as it was in Europe, it was fighting an entirely different kind of war, fighting it with new weapons, and developing new weapons and tools throughout the war when it became apparent that they didn't have all the tools they needed to win the war.

Please feel free to ask any questions regarding my work on the topic that you might have.