Naval Superiority means being able to conduct naval and amphibious operations without effective interference from the enemy, with obvious advantages in strategic choices and mobility. It is important to understand that naval superiority can be obtained by means other than full-scale naval battles: everything can be used to strengthen one's grip on the seas.
Phase One: IntelligenceEdit
First and most important step is to recon and gather intelligence on enemy naval assets. Sonar Beacons on sea chokepoints do well, as do Radar emplacements - which usually have a much longer range, but can't detect anything underwater. Mobile recon provided by Frigates, Submarines, Cruisers, Scout Planes, or Spy Planes can also be invaluable: Frigates usually have radar and sonar coverage, with added bonus (as the radar jamming ability of the UEF Frigate), Submarines have shorter Sonar range and no radar at all, but they can be detected and intercepted only by sonar and submarines or anti-submarine weapons; Scout and Spy Planes rely on long visual range (especially the Aeon Seer) or a good radar/sonar suite (as the Cybran Spook). Cruisers have simply excellent radar and sonar, and are good fleet vanguards. A bit pricey for just reconaissance, but if used properly a Cruiser can be reintegrated into a fleet later.
Phase Two: Submarine warEdit
Second phase focuses on removing any threat on your own naval infrastructure (sonar, factories) and cutting off reinforcements to enemy fleets. While the defensive aspect of this phase is best managed by Torpedo Bombers, due to their extreme speed in comparison with naval units, the offensive is best left to Submarines. Being hard to intercept while underwater, subs can literally sneak by enemy fleets directly into harbors and keep destroying every factory as soon as Engineers try to put another one up, effectively closing off any reinforcement.
Phase Three: "Lepanto" or "Jutland"Edit
Third phase deals with the actual destruction of the enemy fleet. This can be accomplished either by naval or air engagement or, on appropriate maps, land-based missile or artillery fire.
A good hunter-killer fleet is composed by a number of picket ships (Frigates and Submarines), several Cruisers for anti-air defense and direct fire, and a Carrier for recon and pre-emptive air strikes.
Locating the enemy fleet from far away is key. Then, your Carrier launches Torpedo Bombers and Strategic Bombers targeted at enemy ships (in descending priority order: Carriers, Anti-Air ships, Battleships and Cruisers). When the enemy fleet is engaged and starts receiving damage, Submarines sneak in and close on the biggest target for the kill. Then your Cruisers and Frigates join in to mop up the remaining ships. Destroyers with their relatively high HP for a "common" ship are also helpful if they can close to gun range, and the UEF Battlecruiser is very cost-effective when properly integrated, as they are comparatively weak by themselves.
Battleship duels are not too uncommon for players who actually built them, or in very long games. Logically, the best way to counter a massive, big-gun, uber HP, expensive, ridiculous range naval unit is one of your own. They are long and drawn out, due to the 46,000+ HP each ship has, despite their massive guns. Battleships are a huge investment, and the fight won't end until the enemy's fleet is heading for the bottom, as both parties want to keep as many of their huge investments afloat as possible, even if heavily damaged. Usually, the one with more Battleships or more support (air strikes, land artillery, engineers, etc.) wins, though Strategic Missile Subs with their nukes can cause an upset victory if the enemy doesn't expect it, and if away from shore can't be countered.
Note that the UEF Atlantis Submersible Carrier is by far both the largest carrier and the most powerful submarine in Supreme Commander and also that the UEF Governor Cruiser's Cruise Missile makes it deadly in ship-to-ship combat. Plus they have a Battlecruiser, which is basically a cheaper, HP-wise weaker Battleship optimized for fleet combat. In the end, the UEF Navy is the most powerful and is one of the best parts about the faction.