You should normally be able to transfer without selling anything.  You should be able to do a direct-transfer where MS sends your holdings directly to a Vanguard ROTH account.

Talk to the Vanguard people first.  (edited) the Vanguard IRA/ROTH IRA specialists should be able to describe the process to you first, and give you the proper account number and any other routing data needed for the transfer.  And you can describe to the Vanguard people what holdings you have in the MS ROTH IRA account (just in case it does contain something that must be sold first)....all before you talk to the MS people about doing the direct transfer.

If you which to transfer the MS account into your existing Vanguard account, there is no need to establish a new account at Vanguard.  As SteamTrain said, you'll want do the move trustee-to-trustee, not by distribution and rollover; a trustee-to-trustee transfer is neither a distribution nor a rollover and is not reportable on your tax return.  Moving IRAs by distribution and rollover subjects you to the one rollover per 12 months across all of your IRA accounts, traditional and Roth combined.

There is no capital gains treatment for investments in a Roth IRA.  Whether or not you can transfer your existing investments from MS to Vanguard in-kind will depend on the policies of the two firms.  However, except in the case where there is a sales charge, there is no consequence to selling the investment within the MS Roth IRA, transferring the IRA to Vanguard in cash, then purchasing a new investment within the Vanguard Roth IRA.

good points...I missed the comment about already having a ROTH account at Vanguard already (adjusting answer as appropriate).  Still, talk to them first about their transfer policies, and what account information, numbers are needed to give to MS.