The number of fleets a given player can control is equal to that player's planet limit * 1,5. Therefore, a player with a planet limit of 4, for instance, can't have more then 6 fleets. The limit of planets a player can have can be increased through research.
Create a fleet
You need to go to the Ship Yard page. Even if you haven't built it yet, the button appears if you have ships on your planet.
This screen allows you to transfer ships and resources to your fleet, or to your planet. This fleet is currently empty, and you need at least 1 ship to move to another planet.
Type the number of ships and resources you want to transfer to your fleet and click on "Transfer".
Note that you can't transfer resources without a transport ship. In this example you can only transfer the outpost to the fleet. Then, your fleet is ready to move to an uninhabited planet to colonize.