There's an in-game menu you have to use - it uses four directional buttons to navigate. Go to your driving controls to see which buttons are assigned, or change them to something else. Then head out to the track and test out those buttons and you'll see what we're talking about.
As Dimos pointed out, the best time to use the menu to choose tires is right when you enter the pit lane, so you don't need to worry about driving at the same time.