You unlock the Gymkhana Academy after getting 450 total points during the first season. There are a total of 5 tutorials. The number beside the tutorial name is at what point you can find the platinum walkthrough in the video.
1: Smash (0:07)
This one is tricky. Follow the path in the video underneath, and you should eventually get it. If you are having trouble, try revisiting it once you get more similar with the game.
2: Air (1:02)
Probably the easiest of all the tutorials. Just line up with the ramp and make sure you have decent speed and take off straight. Spin you car around to head back the other direction and land 4 perfect jumps, to get 45000+ and get that platinum medal.
3: Drift (1:48)
Very frustrating, but not too bad once you get the hang of it. Again, feel free to come back to this if you are having trouble. The key is to go in a 8-figure instead of an oval. Another key is to score off ALL gates during every corner. Missing a single one will make you get gold instead. Average at least 4,000 a gate, and you should be able to get that platinum medal. If you find yourself having a few bad corners, try rewinding or restarting.
4: Spin (3:05)
Make sure to approach the zone at an angle, hit your brake, turn into the zone, and then apply handbrake and start spinning. As soon as you reach 3 triangles (10,000 points) start heading for the next zone. As long as you make no mistakes, you should be able to make it before the time runs out.
5: Donut (4:19)
The final challenge. Start off with the donut in front of you, and then do what feels right. As soon as you see those 3 triangles fill up, head towards the next closest donut opportunity. Don't waste time, just head for whatever is front of you. After a few tries, this one should come.