Before you can even dream of raiding another planet you need to have several things. You need the Troop Transports and ships big enough to hold them and an engine, you also need troops.
Once you have met the above requirements. Create a fleet of cargo ships and Troop ships (ships that can hold troops) and click the Troop button.
The below screen will appear. Type the number of troops you wish to load into your fleet and then click the load button.
Then once you have flown to the enemy planet click the Troop button and in the box type the amount of troops you wish to drop on the enemy planet then click drop troops.
Once you have dropped your troops the red Ground Battle button will appear...clicking it will take you to the real time log of the battle.
Once you have won the ground battle go back to your fleet screen and click the Cargo button.
Here you can see all the resources on the player's planet and load up to the amount specified in the top. Once you have selected the amounts you want click load and both your Cargo and troops will be loaded back onto your fleet.