First off, you need to build ships,
Then you can go into the "attack" screen, and "browse" for targets
Those who are attackable have a highlighted "attack" button next to them
The number next to the attack button needs to be within +/- 130 as 30% is the maximum allowed Power Rating range allowed unless fedwar or a counter.
To adjust your PR, build or disband ships.
When you have chosen a target and enter the attack screen, select how you wish to attack, Carefull, normal, aggressive and continue. continue again for the attack to commence. Afterwards you will get a status report telling you the outcome and details of the battle.