Start a quick race for at least 3 laps. Simply pit one lap after another on the 1st 2 laps, fitting a different tyre compounds until you have had 3 different compounds fitted. For example, start a race on Softs, pit end of lap 1 and fit Mediums and pit again, end of lap 2 to fit the Hard compound.
To change tyre compounds, you use the in game 'Multi Function Display'.