Maybe you should read the manual, if ou did you wouldn`t be asking that... but anyways:
To fight, you need a few things:
Power rating above 5000, Ships, and, of course, turns.
After you build your ships on the "Build Ships" page, open the ranking and click on "Rank near me". Now you will be able to search around for a potential target.
The people with "attack" marked in blue are the ones you can attack, since they are out of the damage protection.
Note that you can only normal attack people with 130% PR around you and enslave for 150%, unless it is a counter-attack, in which you can attack from any PR. For example, if you have 10000 power, you can only normal attack people with 7693 to 13000 power.
After you choose the desired attack, click on the blue "attack" link. The attack page will be opened, and you can choose the kind of attack you will be doing. Click "Confirm", then you will need to spend 5 turns so you can attack.