Mid-race you can switch tyres when you go into the pits, it'll ask you individually what tyres you want on the front & rear of the car and you'll be able to select from whatever tyre types you've equipped the car with.
Outside of the races, when you're in your home screen looking at the front of the car in the garage, press the "Start" button on your controller to go to the settings screen. Here you can select which tyres to equip on the front and rear of your car, and the type (Racing, Sports or Normal) as well as adjust other things such as Driving Aids, downforce, suspension, etc.
Once you've made changes go back to the garage screen and save the game if you want them to remain next time you start the game up.