I did this recently, rolling a 401K directly into an IRA at Vanguard.
Vanguard has a department that specializes in this. Call them up, tell the person on the phone that you want help rolling over a 401K. He/she will connect you to the right place.
Vanguard initiated a conference call with the 401K custodian, and provided some information to the other firm. I listened, and provided my consent to the transaction. That part took about 15 minutes. It took about 5 days for the funds to show up.
I didn't have to do anything else. This isn't the only way to go, but it was pretty painless.