Starting a wheelie
1° Moving slowly, start on your good pedal, then follow up with an acceleration in your wrong pedal to lift the front wheel while seated. Push-up on the bars just before pulling backwards.
2° Pull back your shoulders as far as possible, with the arms extended and carry on lifting the front wheel until you reach balance on the rear (before falling backwards)
3° Keeping the knees very lose, carry on pedaling slowly. If you tend to accelerate too much, use the brakes slightly so that you don't fall on your back, else push more on the pedals.
See this move in a video You should find a point of balance where you just keep the bike rolling without accelerating. Adjust your balance with the hips. It is easier to learn going up a very smooth slope, then you don't need to control so much the brakes.
At the beginning, if the front wheel tends to drop, it is because you are not enough leaning backwards. For the wheelie, you should reach and feel exactly the same point sitting on your bike, as if you were balancing on a normal chair, on two legs only. Then, when the front wheel drops, a slight pedal acceleration or just pulling your shoulders backwards to reajust your balance. If you fall too much backwards, then you can either crouch forward while folding the arms, or use the rear brake slightly to stay in balance. The mistake of most beginners is to do wheelies by only pedaling and accelerating constantly, instead of finding the right balance. If you can't lift the front wheel at all, it is because your keep too much weight on the front of the bike. By putting your weight over the rear wheel (nearly sitting on the rear tyre), the bike will naturally want to lift the front wheel. To get the move, try to pull so much behind the seat that you fall off the back. From there, adjust the pull.
Once the front wheel lifted, to keep going straight without falling sideways, you must use your knees and waist. For example, if you fall on the left, pull the right knee on the outside, and if necessary, while seated, move the waist a bit aside too. Open the knees more or less outward to achieve perfect lateral control. Control your vertical balance with the shoulders and arms (this adjusts your center of gravity over the rear hub). Really start at low speed and try not to accelerate to stay at a constant speed. Eventually, you'll be able to roll slowly, slow down and carry on again. It really takes some practice but its worth the feel. Initially, it is easier to learn going up a mild slope. This prevents the bike from shooting underneath you and the slope will avoid that uncontrolled acceleration. Once you get the feel for it, improve your braking control, either on the flat or down a slight slope. Launch a normal wheelie, then stop pedaling (manual) and try to stay in balance, only adjusting your speed by braking progressively. To compensate for the braking torque that pulls the front wheel down, you'll need to lean a bit more backwards as you brake.
The 'Manual' is a variant of the wheelie where you carry on rolling without pedalling, while standing. For the manuals, some good pedal strokes for the speed, then lift the front wheel and stay in balance on the rear wheel. Keep your bum above the rear wheel axis and control the whole bike inclination with your arms and knees.
In a very well balanced manual, you don't even need to touch the brakes. Then a bit more complicated, is to land a bunny hop directly in manual (instead of a blunt stop) to carry on rolling smoothly on top of an obstacle. This brings a more urban BMX style to trials, stylish although never ever used in time trials. But hey, let's have fun too. This move requires excellent balance control, as you have to roll perfectly over the step you climb (while avoiding a crash on your back). Keep a finger ready on the rear brake, just in case.