Learn the wheelie: pedal kick, arms extended, sweet spot over the rear hub, rear brake as a safety. With milestones, mistakes and safety.
The honest answer: a wheelie is riding on the rear wheel: you build momentum with a low upper body, extend your arms dynamically, pedal hard and then balance around the sweet spot, where your centre of mass sits roughly over the rear hub [1]. The BASPO, the Swiss Federal Office of Sport, states: on the trail the wheelie is rarely used. But it is the basis for many other riding techniques and promotes balance and feel for the rear brake like hardly any other technique [1].
How hard is it really? The BASPO itself writes that the wheelie is not so easy to learn and demands a lot of patience [1]. You need weeks of short sessions before you manage a few metres (rule of thumb, not a study value). That is normal.
And it is not harmless. In a video analysis of 534 mountain bike crashes, backward falls were rare at 3.2 percent [2]. But they are exactly the risk in a wheelie when the front wheel comes up too high and the bike tips.
The wheelie is less a trick than a balance test that you pass in small steps.
Find grass or firm, smooth ground, flat and open. Soft ground forgives small falls, smooth ground gives even resistance.
Milestone: you can roll the area in one lap and know where the limits and obstacles are.
Sit on the saddle and pedal loosely. Keep tension on the chain so the pedal kick works later [1]. Your gaze goes straight ahead.
Milestone: roll 20 metres evenly seated, eyes straight ahead.
Bring your upper body low toward the handlebar and bend your arms. Then extend your arms dynamically and pedal hard at the same time so the front wheel lifts [1]. Afterwards your arms stay extended.
Milestone: the front wheel lifts a few centimetres and lands softly without the bike tipping.
The sweet spot is the point where the bike is balanced. Your centre of mass is then roughly over the rear hub [1]. You feel it when you hardly have to pull or pedal.
Milestone: you hold the point for 2 to 3 seconds (practice).
You vary the front wheel height with pedalling and measured use of the rear brake [1]. One finger always stays on the rear brake [1]. Sideways corrections come from knees and shoulders: if the bike tips right, spread your left knee out to the left and tilt your shoulder slightly left, and vice versa [1].
Milestone: 10 metres on the rear wheel without having to put a foot down (practice).
In a wheelie a fall backward threatens. Backward falls are rare (3.2 percent in a video analysis of 534 crashes [2]), but the back of the head, wrists and tailbone are exposed. In mountain bike injuries the head and upper extremity are most often affected [5]. In a meta-analysis of cyclists a helmet reduced serious head injuries by about 60 percent [4], a guide value for cycling in general.
Never practise on slopes, near roads or on wet ground. If you tip over, do not let go of the handlebar, pull the rear brake and put your feet down (practice). Learn to step off before you tip. This guide explains and motivates; it does not replace supervised training.
Practise the sweet spot in place: roll at walking pace, lift the front wheel and let it sink with the rear brake, without pedalling. This teaches the feel for the balance without the bike rolling away. Pedalling comes afterwards.
Balance on the bike helps too. In a study of 29 mountain bikers, bike-specific balance tests were clearly linked to riding performance (r up to -0.78), while standing on one leg hardly was [3]. The wheelie is exactly such a test.
Pedal loosely seated, upper body low toward the handlebar, then extend your arms and pedal hard. You hold the sweet spot with pedalling and the rear brake [1]. Practise on flat, soft ground and in short sessions.
In a wheelie you pedal and balance on the rear wheel [1]. In a manual you roll on the rear wheel without pedalling (common coaching definition). The manual is considered harder because you hold the balance without a pedal impulse (practice).
You pull too hard or pedal too hard. The rear brake solves the problem: pull it smoothly when the front wheel comes up too high [1]. Lift the wheel only a few centimetres until you get the feel.
No, the BASPO writes that it is rarely used on the trail [1]. It is worthwhile as a school for balance and braking, especially as preparation for the manual and obstacles.
Rear Wheel Pivot on a Mountain Bike: Ride Tight Switchbacks Without Dismounting