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There's several tricks in Moon Surfing, more than the basic three that most surfers will find. They haven't been documented anywhere before, but it's also fun to discover them for yourself, so this seemed like a good compromise.
I'll be using a combination of surfing, skateboarding and miscellaneous names to refer to them. They're also organized by difficulty - while the harder tricks have stronger effects, you'll likely find yourself using the easier ones most because you want something reliable for split second actions like going off jumps and carrying your momentum up a slope.
Easy
Jump - Release your finger. No cool movements, the board just allows itself to enter the air. Taught in the tutorial, but you won't be using it for long since it doesn't do anything special.
Hang Ten - Swipe upwards. The board is held up on one side. Gives you a bit of upwards lift, and a bit of extra speed. Good for going off of ramps.
Kickflip - Swipe left or right. The board will roll in the direction you swipe in. Gives a great deal of sideways momentum in that direction. One of the most important tricks, maybe even more than the regular jump. It's a bit broken if you know how to use it right - you can spam it on the side of a hill to get easy air time, or do a few kickflips against the side of a steep slope and then kickflip in the opposite direction to fly high up in the air.
Medium
From now on, the tricks are performed by a series of inputs rather than one. You need to keep holding your finger down through each input. You don't have to do all the inputs within a specific time window, so if a trick is being tough to figure out, feel free to slow down your finger movements to get the hang of it!
Boardslide - Swipe down, then left/right. This trick turns your board to the side, with the back end facing the direction you end the trick in. It gives a speed boost, like the hang ten, but it keeps all of that extra speed better when moving through the air. Contrary to how it looks, this trick doesn't change your hitbox. Use it when going down a large hill and it'll be your best friend.
180° - Up, then down. A quick spin on the yaw axis. Alternatively, down then up - the direction you spin is oddly randomized regardless of which way you do it. Gives lift, much more than the hang ten. A strong contender for going off of ramps, and a skilled surfer can use this to effectively bounce off of rocky slopes.
Hard
Quad Kickflip - Either left-right-left, or right-left-right. A huge roll. The direction you end your swipe in will determine which way it rolls. This trick actually slows you down a bit when you use it. However, it's extremely floaty and has a habit of generating air time out of basically nothing.
360° - Up-down-up. Makes the board spin several times clockwise. Down-up-down makes it spin counterclockwise instead. This gives equal lift to the 180°, but adds a bit of floatiness.
Extreme
Breakdance - There are a whopping four different ways to do this trick... For starters, up-down-up-down-left makes the board spin clockwise on the yaw axis, while spinning on the roll axis at the same time. Input up-down-up-down-right, and the board will breakdance counter-clockwise instead. Down-up-down-up-left or down-up-down-up-right will make the board breakdance clockwise and even throw a few extra rotations in. It's honestly hard to say what this trick does. Judging by how the camera shifts, it seems to gain speed and possibly also lift while it's in the air. But it's certainly the coolest-looking trick out there.
