There are two places where you can assign a driver, through the reservation or the dispatch list view.
Assigning a Driver Through the Reservation
Go to a reservation requiring a driver. Click on Add a Driver and select a driver from the drop-down.
Assigning a Driver Through the Dispatch List View
From the dispatch list view, look for the driver column. From this column, you can double-click on the driver section of any reservation and assign a driver from the drop-down.