Overpower Their Battleships
Use your Battleships to destroy theirs. Use Battleship and Juggernaught Control Techniques to overpower them. An Alternative is to use Submarines to take out the Battleships then use Battleships to finish things off because only they can destroy Peons repairing the Foundry and Shipyard and Catapults protecting them.

Destroy the Oil Rig
The fastest and most damaging thing you can do to the enemy early in the game is destroy their Oil Rig. The Oil rig cannot be speed repaired by Peasants or Peons and it must be defended while it is being built. Losing an Oil Rig means the enemy can only build a few more ships before they run out of Oil. In some cases the enemy will run out of Oil and may not be able to build a Blacksmith or upgrade to Keep or Castle.

[ Click to Enlarge - 45 KB ] A Battleship attacks an enemy Oil Rig as it's being built.

Destroy the Foundry
Once the Oil Rig is destroyed, destroy the Foundry. If you don't see it around the Oil Rig and Shipyard, start attacking the Shipyard and send some fast moving ships such as Destroyers to find it. Then once it's found, abort the attack on the Shipyard and go after the Foundry. If you destroy the Foundry they will not be able to make Battleships or Transports. Be sure to keep a Destroyer by the Shipyard to "Lock-on" any Transport that might pop out at the last minute.

Take the Enemy Off the Sea
Over power them with Battleship and Juggernaughts destroying their Oil Rig, and all Sea Buildings.

Use Destroyers to Kill Transports
Immediately, build 2 or more Destroyers to get any Transports that are already out there, or that the enemy might build before their Shipyard goes down.

Keep Them Off the Sea
Keep the enemy on their island. If you can keep them there, their resources will run out. When the enemy's resources run out it will be just clean up time.

Prevent the Enemy From Getting Oil by Guarding All Oil Spots Surrounding the Island
The enemy will most likely try to build at another Oil spot around the island or the same one. Place a Battleship or Destroyer just on the other side of the Oil spot. If the enemy builds a Shipyard, they will most certainly try for another Oil Rig. The second that Oil Rig goes up, your Battleship/Destroyer on guard will start firing at the Oil Rig alerting you. You can also place Oil Tankers over the spot or you're ships over the spot. You can even build Oil Rigs on their Oil spots. Decide what to do based on the closeness of the Oil spot to the enemy island. If Oil Spot within Blizzard range THEN place ships on the far side of the Oil spot. But if Oil spot out of Blizzard range, simply place your ship on the spot. You can also place a Submarine under the Oil spot. That really confuses the enemy if they don't have a Flying Machine nearby.

Does the enemy have enough Oil to make Transports if they rebuild their Shipyard? If they have a lot of Oil, you may be in trouble. Build more then 2 Destroyers and place them around the island. Place Flying Machines all around the edge of the shores. If you see a Shipyard going up, go destroy it. If the enemy can defend their shipyard, defense, let them build it but cut off the Oil and have Destroyers ready to lock on any Transport that is built.

Discover If They Were Able to Get Off Their Island
As quickly as possible, get some Flying Machines and make sure the enemy did not get off the island and build somewhere else. If they did, take care of their new setup as quickly as possible. The more time they have to set up defenses, the more difficult it will be to get rid of it.

Prevent the Enemy From Getting a Second Mine
Watch the Gold Mines with Flying Machines on patrol and make sure to quickly put a stop to any enemy building by them.

Get a Second Mine Yourself
Make sure to expand to several islands. Defend them with walled in Towers. Build Barracks there to further reinforce the islands.