When talking to the Tavern Owner about work you can get 2 easy missions for a bit of reputation and gold. These are generally not worth doing unless you're desperately in need of gold.
Passenger[]
He will tell you about a guy who wants to go somewhere, and the passenger will appear and tell you where he wants to go and how much he will pay. Note the time limit he gives you to reach his destination because if you exceed the time limit, your reward will be reduced. Get him to his destination, go to the tavern, and he will speak to you and give you your reward.
If you exceed the time limit, he will come aboard your ship and ask you why you're taking so long. At this point, you can reassure him he'll get to his destination (but you'll get reduced pay) or you can enslave him, which will of course reduce your reputation.
BUG: It is possible for him to bug out if you enter the tavern and somehow fail to let him talk to you (such as talking to another person immediately instead). In this case, you will never receive your reward.
Escort[]
Escort is the same as a passenger, but the difference is that he actually owns a ship and as such, you'll need to have at least one ship slot full. If you accept, you'll get another ship in your squadron and will have to protect his ship throughout the journey. When you finally reach the destination, he will meet you right after you moor, so speak to him and collect your reward.