Do I get to hold the stock itself with a restricted stock grant?
Usually the shares are legended with the restrictions, and they are often held in escrow with your company's transfer agent or in some type of custodial arrangement until vesting. Companies often issue the escrowed shares electronically, though some companies issue the stock in certificate form. Once your shares vest, they are released to you. Ask your company about its exact procedures and how withholding taxes are paid.
Alert: Before requesting a paper stock certificate in a public company, find out whether there are any fees. With the move toward getting investors to hold stocks in electronic form, brokers and transfer agents are charged a fee by the firm Depository Trust and Clearing (DTC), which tracks ownership and transfers, and your agent may pass on the fee to you.