John, when the driver before you pits in, they will come to a stop in their pit box and hold Esc. to get out of the car. As soon as they are out of the car, there will be a green "Drive" button (the same button that says "Grid" or "Drive" in Race/Practice) that will appear for every member of the team. If it is your stint next, than click the drive button and you'll be put into the car.
Important: When a driver stops in the pit stall, everyone spectating that team will have a yellow button, instead, saying "Remove Driver".
DO NOT PUSH THIS BUTTON!!
Pushing this button WILL pull the driver out of the car, but if you try to "Remove Driver" at the same time the driver is trying to Esc. out of the car, than it could crash the game or glitch your pit stop!
There is no rush to this process! It takes all of 5 seconds of holding the ESC. key to be removed from the car, and the same amount of time for the next driver to push the button and get into the car. The entire pit stop takes 30-50 seconds, so take your time. Make sure, if you need to make any adjustments from the previous driver (Brake Bias, TC1/TC2, etc) that you make those changes before leaving pit road.
If you have any questions, your team will happily walk you through it!