You have to be in port. Click on one of the ships you want to move to another fleet, then click on the detail tab. At the bottom you should see a choice for moving the fleet to another fleet if one is present or creating a new fleet. Click on move, a screen will pop open with any other fleet captains present. Click on the captain whose fleet you want to move the ship into, then ok. Your ship will now be part of the other fleet. I have only done one at a time. I don't think you can move multiple ships at once.
Hope this helps.