In Civ2, subs stink. Put cruise missiles on your subs and have them travel in groups. Attack lone warships or transport away from reinforcements. One sub attacks, others act as backup and retaliation if first sub is attacked. The best way to use subs is to keep them close to support of other surface warships. A good strategy is to keep them in ports and attack enemy ships next to your port. Subs with low speed and defense were not made to function without support for long. I don't really recommend building any subs since AEGIS cruisers are much more effective in staying alive and low range missions.
My strategy for modern ships:
Destroyer-Patrol, recon, ASW, decoy for AI ships, expendible. Put them in between AI ships and your own to slow them down if situation is desperate.
Cruiser-Attacking threats near waters of your nation, ASW, escort for transport. These are most of my navy to protect my waters from invasion and escorts.
Battleship-Protect with other warships, coastal bombardment. Low speed makes this not so great as a warship, but a mobile seige machine.
Submarine-Attack/retaliate against warships, put in port, put back into port at end of turn, expendible, useful against unescorted transports or close warship alone in the water. Use these if the cruisers weren't enough.
AEGIS-Best ASW, effective ship killer, some shore bombardment, escort for carriers/battleships against air strikes. These are the best ships in the game, they're fast, strong at attack and defense, can operate in enemy waters longer than most other ships, seek out and kill other ships.
Transport-use to land invasion troops, escort if loaded, put troops on multiple transports as insurance, travel behind warships, move forward only if invasion route is secured by warships, stack with more powerful ship.
Carrier-Expensive on resources to load up and build, carrier battle groups with bombers are most powerful force on the sea. Use bombers and stealth fighter to provide close air support for invasion forces.