Sea battles are the main form of combat in the game. Escort ships of both parties in combat engage one another in gunnery duels.
Prior to engaging in a sea battle, you must have escort ships, and they need to be properly armed for ship combat.
As escort ship is simply a ship that has been designated as a combatant in sea battles. Of the ten ships maximum in a convoy, up to five may be designated as escorts. Non-escort ships cannot participate in combat.
Escort ships need armaments in order to be effective in sea combat. At a minimum, each ship needs cannons, and the convoy needs ammunition for the cannons to be able to fire. You probably want enough cannons to fully equip all of your escort ships, and at least twenty or thirty units of round shot as an absolute minimum (you'll want more than this, though you can possibly scavenge from captured ships). Having more types of ammunition allows for different tactics during battle.
You will also need sailors to both protect your ship from being boarded, and to perform your own boarding attempts. It's also worth buying your sailors cutlasses to maximise their boarding effectiveness.
Types of Convoys
There are several different types of convoys you can attack. You can attack by simply right-clicking a target - the target will flash upon being selected (when you close to range the game will ask you to confirm the attack).
Trade convoys have a flag of nationality with a white background. These are often unescorted, which allows for an easy raid, or they may have a light escort, which will require some force to overcome. Either way, trade convoys can be looted for whatever goods they carry. Attacking a trade convoy without a proper Letter of Marque is piracy.
Military convoys have a flag of nationality with a solid colour background. These comprised mainly of warships, so you'll generally either be attacking them to weaken the country in question or be on the receiving end of attacks from them if they declare hostilities against you. Attacking a military convoy without a proper Letter of Marque is piracy, although you are well within your rights to defend yourself if you are attacked.
Pirate convoys have a skull with a black background. They are similar to military convoys, but more tenacious (if less well armed). Pirates will raid your trade convoys without provocation. If you are attacking a pirate, you don't need a Letter of Marque since pirates are outlaws and thus not protected by the law anyway.
Occasionally a quest will require you to defeat a special convoy such as an Adventurer (especially during rescue missions). This convoy will appear to be a normal military convoy, but it will attack non-trade (i.e. manually commanded) convoys on sight. Since you are technically defending yourself in the battle, there is no diplomatic penaity.
In combat, you will sail one ship at a time against your enemies who, sadly, can use all escorts at once. Your objective is to cause all escort ships to sink, surrender (via boarding) or retreat from battle. You control your heading with right mouse, and fire cannons by clicking targets beside the boat, or by pressing the "s" key (by default) when the target indicators appear on enemies beside the boat.
You can select from your ammunition types by clicking the ammunition buttons. You may also prepare for boarding by clicking the cutlass button. After each order, you must wait for the circle to fill before firing or boarding. You must also wait after firing for the cannons to be reloaded.
Upon boarding, the crew members of the ships will commence battle. A popup will appear showing the progress of the battle. When either side's crew members are eliminated, the ship is considered captured. A ship not prepared for boarding is at a disadvantage during a boarding operation; if your enemy appears to be attempting to board, it may be best to prepare your own ship if you are able to do so in time to negate his advantage. If the ships make contact but neither side is prepared for boarding, this combat will not occur. If the ships are of relatively equal strength, you will often be challenged to a swords duel - the losing captain's crew will surrender without a fight.
If your active ship is sunk, captured or retreats (by sailing outside of the battle area), you will be prompted to select another ship to continue combat. If you do not select a ship, or have no ships remaining, you lose the battle. Escort ships that escape remain under your control, but captured and non-escort ships are at the mercy of the enemy. If all enemies are sunk, captured, retreated or a combination thereof, then you control what will happen with them (see below).
Profiting from Encounters
If you win a sea battle, any boarded ships, and any non-escort ships, are at your mercy. You may choose to raid any goods on board, and you may choose to capture or sink the ships themselves. Captured ships can be sold, or repurposed into your own fleets. Conversely, you might leave the ships intact, returning them to their original owner, which minimises the diplomatic penalty with the nation in question (nations are not impressed by having ships raided, but having ships captured or sunk will truly anger them). Pirates have no protection from nations so there is no point in leaving any ships intact; any ships should be either sunk for a reward or captured to either sell or repurpose.
Letters of Marque
Under normal circumstances, attacks against convoys (other than pirates) are considered acts of piracy, and decrease your relations with all nations. During wartime, governors can issue Letters of Marque. Each Letter of Marque is valid against a given nation, and it gives you privateer status for the duration of the war, allowing you to legitimately attack that nation's convoys without risking universal hatred. The country you attack will still dislike you, but the country who issued your Letter will appreciate the effort, and third parties will ignore the attacks.
You may purchase Letters of Marque from governors of towns whose nations are at war. They may also be automatically issued (for free) if you accept a quest which requires you to possess said Letters. Letters of Marque are good for the duration of the war; when a peace treaty is signed between the two nations your Letter is rendered void. This means if you wish to continue hostile actions against the nation without universal diplomatic penalty, you either need to approach another nation (one still at war) for a Letter, or wait for another war to break out and then renew your Letter.
The encounter screen will remind you whether or not you possess a Leter of Marque when you are confirming an attack. Note that while the screen will inform you that you don't have a Letter of Marque against a pirate, remember that you don't actually need one. You also don't need a Letter of Marque if you are attacked, yourself; you always have the right to self-defence.
Letters of Marque also permit you to raid towns belonging to the target nation.