Backdoor Roth

A Backdoor Roth IRA is a technique for contributing to a Roth IRA when your income exceeds the contribution limit. There is no income limit on contributing to a nondeductible Traditional IRA, nor on converting a Traditional IRA to a Roth IRA.

Mechanics
To make a backdoor contribution, first make a regular contribution to a Traditional IRA with your IRA custodian. You do not specify to the custodian whether the IRA is deductible or not; it is just treated as an IRA.

As soon as the contribution posts, convert to a Roth IRA. To do this with Vanguard, you buy shares (or open a new account) in a Roth IRA, and fund it by "selling" shares in your Traditional IRA. Since your initial contribution was non-deductible, you pay tax only on the difference between the converted value and the amount contributed, and since you held the Traditional IRA for only a few days, the tax should be trivial. Thus, even though you are over the limit, you are in essentially the same situation as if you had made a contribution to the Roth IRA.

Caution
If you have any other (non-Roth) IRAs, the taxable portion of any conversion you make is prorated over all your IRAs; you cannot convert just the non-deductible amount. In order to benefit from the backdoor, you must either convert your other IRAs as well (which may not be a good idea, as you are usually in a high tax bracket if you need to use the backdoor), or else transfer your deductible IRA contributions to an employer plan such as a 401(k) (which may cost you if the 401(k) has poor investment options).