You can add an additional driver to the rental agreement at pick up time. Both the primary driver and the additional driver must be present to officially sign the rental agreement. The car rental company will determine the rate for additional drivers.
Please note that some car rental companies will not permit an additional driver unless he/she is over the age of 25 and has a valid credit card in his/her own name. There may be restrictions regarding adding an additional driver if the primary driver is using a debit card.