It is important to cover your island hopping campaign with land-based air support. Capture an airfield, improve it, then transfer planes to fly Combat Air Patrol and move on to the next base.
Reconnaissance
Reconnaissance is very important. The first side to locate and subsequently attack an enemy battle group is often the side to emerge victorious.
Supply
Hindering the enemy's line of supply is crucial for victory. Check enemy supply routes each turn, and direct your submarines to straddle the routes.