To raid is very simple: Have the captain of a ship go to the ship's cabin, and click "Raid the coast". The page will load with a list of what has happened to the crew. It is recommended that you send in submissions about how well you did on your latest raid.
You have to raid or explore before you can return to port, and when you do it is up to you. The general scenario, which has an equal chance of doing well or badly, is a ship with a profit of 1,100 G, 12 crewbeasts, and about 1000 merriment. Do better than that, and you have a good chance of getting a great deal of profit. Do worse, and you have a good chance of getting a great deal of sick points.
Your success at raiding is calculated based upon your Ship's Offense, which is calculated by the following:
Offense = (Morale - (# of Shipmates*35)) * (# of Shipmates) + Profits This Run - (Number of Submissions Since the start of This Run*10) - Days at Sea;
What does it mean?
Each raiding event has a certain amount of good events (shown in green) and bad events (shown in red). When good things happen, such as looting a certain amount or finding food, the crewbeast who did it will get half of the loot, while the other half goes to the Imperium. If you kill a woodlander, multiply the woodlanders by 5G, and that is how many gilders it was worth overall - the crewbeast still only gets half. When something bad happens, such as getting hit by a woodlander of stumbling, the crewbeast who had found their misfortune will get added sickpoints.
As your offense grows, so does the maximum amount of gilders (and sickpoints) you can get.