To move a fleet or resources from one planet to another you need to land on the desired planet (either make it active from the left menu if you are in space mode).
If you are on the surface of the planet, you need to move to the «Star Map» (1).
Next, you need to choose the planet to which you want to move the fleet.
Click on the planet and select the «Support» parameter in the window that appears
Now you should choose the number of ships that you want to move to another planet.
Similarly, you can move minerals to another planet if you have transport ships. To do this, click the «Transportation» button