More detailed Instructions:
Always park the Brompton bike by swinging the rear wheel under before folding.
Always fold back the front wheel assembly before folding down the seat or handlebars.
First make sure that the right hand pedal is out of the way of the front wheel. It is best if the right hand pedal ends up pointing backwards and downwards.
Unscrew the hinge clamp on the main frame until the locking plate is free (three or four turns of the handle normally suffice). Grasp the handlebar support, lift slightly (maybe pushing back on the saddle at the same time) and, keeping the front wheel pointing forwards, use a "stirring" action to move it out and back round till it lies alongside the rear wheel (again no strength is needed for this, but if it helps, take hold of the front mudguard with your other hand and guide the wheel round).
Make sure that the hook has passed over the tube on the rear frame, and allow the front wheel assembly to drop (the whole bike actually rotating relative the rear frame). The front wheel is now in its folded position, and you can proceed with folding the remaining items.
Handlebars and saddle (and folding pedal):
Undo the hinge clamp at the base of the handlebar stem; swing the handlebars down to lie alongside the front wheel and push home so that the nipple engages in the clip. Alternatively, simply let the handlebars drop into position on their own.
Undo the lever and push the saddle down. During this action, the lower end of the seat pillar passes behind the plastic disc on the rear frame, and it is because of this that the rear frame remains folded, in turn retaining the front wheel in its folded position. So if you do not push the saddle down fully, it is possible for the folded package to come apart when you pick the bike up. You may wish to use the saddle as a handle to carry the bike, and in this case, you should reclamp the seat pillar using the lever.
It is best to fold this with the left hand crank as high as possible (i.e. with the cranks turned so that the right hand pedal touches the front wheel). Rotate the pedal so that the ridged side of the latch plate is pointing upwards; next press the outer part of the latch plate downwards, so that the inner part clears the top of the bearing housing. Lift the pedal body and stow the pedal.
If you find a faster method, feel free to use any way that works best for you.