I read that most of the ships were initially very vulnerable to aircraft, and that they were equipped with an increased number of anti-air guns accordingly. But beyond that, what was the strategy for dealing with air attacks? Did they use ships dedicated for the purpose of defending the bulk of the fleet from aircraft? How successful were they in shooting down or deterring attackers with AA guns when they could not intercept them with aircraft?
Yes while most large ships from cruisers on up were equipped with AA they were lacking by late war standards.
In large part though the way the USN protected surface ships from air attack was to not have them operate without a carrier.
From Pearl Harbor till 8 months later at Guadalcanal the only real sizable formations and operations undertaken by the USN focused on carrier raids or countering IJN ones.
A carrier task force would have the carrier, 2-4 cruisers, and 4-6 destroyers. The carrier in the center with the other ships in a circle about 2k yards out. This could be very effective, US fire control was much more advanced than contemporary IJN. Same with Fighter Control auded by radar for the CAP. Carrier task forces early war stuck to doctrine of operating singly and detached to not all be destroyed at once, but also spreading Defenses thin. AA would contribute but the more effective solution was always the fighter plane, though wartime kill claims sometimes obscured that.
Certain ships were used and valued for their support value. The Atlanta class CLs and their oodles of 5in guns. Also the new fast Battleships, the North Carolina gave very valuable service with the Carriers of Guadalcanal. Often described as either looking like a Christmas tree or fireworks show from all the fire it was putting out.
Would HIGHLY recommend the First Team duology by John Lundstrom for an overview of early war battles.