There are basically three ways to free yourself. First, and easiest, restart your empire. You probably don`t want to do that. Secondly, you can ask the person that enslaved you to release you. That often doesn`t get results. The "best" way for most people is to get your Power Rating to 10x that of the empire that enslaved you. If you click on Slave Empires and the V next to your slavemaster`s name, you can see his/her pr. Multiply that by 10 to see how high you have to go. If you can afford to build enough ships to get to that high of a pr, then do it and you`ll be free. If you`re in Damage Protection, you should use starbases. If your not, then just build ships until you hit that mark, then go back to Slave Empires page and click the Free Yourself button.