To get arrested, just pick up anything that doesn't belong to you, get 1 or 2 gp bounty (a notification pops up) and then turn yourself in to the guard and tell them you'll serve time.
Jail locks are Adept level, which means they're somewhat tough. Standard procedure is that you get one lockpick, if it breaks then you have to wait out your (short) jail sentence, and more importantly you miss your chance at this achievement until you get arrested again.
If you're already a decently high level by the time you do this, it may be pretty easy. The "Adept Locks" perk requires 50 ranks in Lockpicking, and makes these level locks easier. The "Locksmith" and "Unbreakable" perks require 80 and 100 ranks respectively, and if you've got all those then you really won't have much trouble with the lock-picking part of this.
Not every jail is the same:
- Riften's jail cell has a lockpick sitting on the table, so you'll get two to work with
- Dawnstar's jail cell has a Lockpicking skill book in the corner. Not a huge help, but it's also probably the smallest jail building so the getaway is easier.
Don't forget to grab your gear at the chest on the way out.
Addendum: Oddly enough, I got this achievement from somewhat of a glitch. I was imprisoned in Solitude, and before I could even try to pick the lock a guard materialized in my cell and walked out. Of course he had to open the door to walk out, so I followed him. Since I didn't pick the lock, no guards were hostile and I just walked right out of prison for 10G. No idea how reproducible that method would be though.