I'm assuming you know how to ride a bike, but maybe you're not that trained in it. This guide's for you. All of this is very, very easy to learn. I won't tell you to do sick bunnyhops.
All of them can be learned in an empty car park or streets. These are good techniques to put less strain on both your bicycle and you and especially your most treasured body parts (the ass).
1. Riding while Standing
I see a lot of people having a bit of an aversion to this, but it is one of the more important ones, especially for other techniques. Learn how to ride your bike standing up out of the saddle. If you're on rough terrain, it's nicer and safer to not have your seat ram you in the ass.
Don't shift while doing it unless you know what you're doing and if you have to brake, lean backwards.
Empty street or car park, and get a feel for it. Start by hovering your ass slightly over the saddle and then go from there via incrementalism.
2. Pivoting your bike over bumps.
Okay, you learned number 1. But if you're stiff as a board over potholes and bumps, it's still gonna be a shakey experience.
But if you're standing up, you only have two contact points with your bike instead of three - handlebars and pedals. And luckily, they're connected to the bits on your body that can do dampening.
Find a small, rounded obstactle like a speed bump and definitely not like a curb and learn to anticipate the forces it will enact on you. With some training, you can basically keep your body position mostly the same and use your arms and legs to dampen the impact and shift your way weight around as appropiate so the impacting wheel takes as little of it as possible.
What you want to aim for is your head keeping it's place on the vertical scale as your arms and legs feather the bump for you. Your bike goes up and down, you don't.
For the US folks, you know how Motorcycle Cops do turns? Do that.
3. Counter-Lean
It's a two wheeled bicycle, lean left to go left, lean right to go right, right?
Okay yeah, sure, at speeds. Probably much greater speeds than one usually gets in every day riding.
Enter the counter-lean. Especially on shitey, narrow bike paths this can be a life saver. Can be done while sitting or standing. Imagine your torso fixed in it's current path, and then you just move the bike under you by angling. This is the quickest way to do small deviations from your current path, as you don't have to heave your entire body left or right. Imagine like someone on skis or a snowboard doing carving, you wanna do that.
To learn this, I'd advise trying to do meandering turns somewhere you can do those while keeping your body upright and the bike at an angle and then, again, work your way up there where you can do it at speed.
4. Front Wheel Lift
So you're approaching a curb or something you can't avoid and gotta get over but bunnyhops without being clipped in to the pedals are too hard (they are too hard).
What you want to do to alleviate some of the forces enacted on your wheel is do a front wheel lift so you don't transfer all of the energy of going up a curb into your front wheel.
You wanna be standing up for this. If you don't have front suspension, just pull up a bit.
But if you have front suspension, that's probably gonna leave the wheel on the ground as the suspension takes the force. What you want to do is push down, and then use the returning momentum of it to pull up.
So again, you're on the empty street. Either pump or give it a bit of a tug until you get some slight lift. Don't overdo it or you're gonna go over ass backwards, work your way into it. Once you've got it, approach a curb at low speeds and then just try it on there. And then, again, work your way up. Just be careful so you don't eat shit.
Bonus points for shifting your weight forward when the rear wheel hits so it takes less force.