So now that I have been arrested for murder, how do I get out of this prison?

start talking to the inmates there.

I warn you though, DO NOT DROP THE SOAP!

Follow the quest line while you are in there and make sure upon escaping, to not interfere and kill the guards, but feel free to slaughter your fellow inmates once you are out in the city. Ive bugged my game with a permanent bounty by being a bit overzealous and slaughtering the guards. There is no reason to side with the forsworn.