A lot of visitors come here by Googling information about transferring their retirement accounts, either the IRA or their Roth IRA, many to Vanguard.
Since there seems to be interest in the topic, and I just completed my Roth IRA transfers from Ameriprise to Vanguard recently, I'll recap the entire process.
Open an account with Vanguard at https://flagship.vanguard.com/VGApp/hnw/OpenAccountController
To fund it, you'll want to transfer your assets from your current brokerage. Make sure you have your most recent statement nearby, with account number, ballpark funds etc.
You'll have to pick out the funds you'd like to buy into with Vanguard, then fill out a transfer form.
Vanguard will ask you the questions and fill out the form for you. You might need to get a medallion signature guarantee from your bank on the form.
You'll send the form to your current brokerage, who will transfer your money (and probably take a transfer fee off the top … argh) in a few weeks — expect up to 6 — and then you're good to go.