#1. Take out all forts (7 total).
#2. Look for the fellow that offers the naval contracts and talk to him. Each fort has one, some have two contracts to give.
#3. While you can start these at any time, it would be best to wait until you get some upgrades. If you playing this for quick achievements, go after it. If are in it to totally wipe the game, wait until much later when you have a few major or even epic upgrades. The last one, which you get when all others are done (Seranillas) can be a major doozy if you are unprepared.
#4. As a bonus, you can help yourself with the upgrades by boarding the ships that you hit, which will only make you better.
#5. Be careful not to drag in other ships into the fight that are not a part of the mission.
#6. Some of the contracts require you turn over some loot (cloth, wood, rum). If you have those already in your ships inventory, you can turn those over immediately earning you to contract reward.