[Dogfish40]

Welcome aboard.
There are a lot of people on this site who can help out.
When you get to the area you're supposed to patrol you'll see a Yellow Star with binoculars on the navigation map. (Binoculars or a camera depending on the type of orders for the patrol). You need to patrol within 70 or so N'Miles of that star for roughly 48 to 72 hrs sometimes longer sometimes shorter until the star changes color (to grey). If you leave the area of the patrol star it usually will not change color, meaning the mission is incomplete. However, I personally have had mixed results by sinking a lot of ships and leaving the star (or the area) incomplete.
Anyway, if you go back to you're mission area and stay there within 70 or so N'Miles, it should change to grey and you'll get a message that the mission is complete.
Guys, if I've missed anything, please chime in.
Whoops, My bad. I thought you were asking about ending the patrol orders. Yes, to actually Dock and end your patrol, you will need to go to your home base with the tilted anchor as Jan mentions.
D40
PS; Way to go w' Tokyo!!