With RSUs, you are taxed when the shares are delivered, which is almost always at vesting. Your taxable income is the market value of the shares at vesting. You have compensation income subject to federal and employment tax (Social Security and Medicare) and any state and local tax. That income is subject to mandatory supplemental wage withholding. Withholding taxes, which for U.S. employees appear on Form W-2 along with the income, include the following:

federal income tax at the flat supplemental wage rate, unless your company uses your W-4 rate
Social Security (up to the yearly maximum) and Medicare
state and local taxes, when applicable

A company may offer a choice of ways to pay taxes at vesting, or it may use a single mandatory method. The most common practice is taking the amount from the newly delivered shares by surrendering stock back to the company. This holds or "tenders" shares to cover the taxes under a net-settlement process, and company cash is used for the payroll tax deposit.

When you later sell the shares, you will pay capital gains tax on any appreciation over the market price of the shares on the vesting date.