with the sheep chair, you just back them up until their hind legs hit the bottom bar, then back them up one more little bit and they'll "sit" in the hammock part of it. lift their chest and lay them back into the chair - feet up, all is good! mostly they don't fight if all 4 feet are clear of the ground. if they can feel a hoof on the ground, some of them will scramble to try to get up.
to do it without a chair, stand with sheep facing your left, you're at it's shoulder. put your right leg behind their hind legs, your left forearm/hand at their chest under their neck, and your right hand on their butt. while pushing down a little on their butt with your right hand, using your left arm, back them up until they sit - your right leg will stop them from steping back so they'll put their rump down on the ground. then lift at the base of the neck/chest so they're fully up on their rump and lean their body weight against yours. I can do this with all but my big rams (for them, I need a second person).
if they're fighters you can turn their nose to their shoulder before you back them up.
pop on youtube, you're sure to find some video of sheep sheering - watching the pros do it is cool - they're very quick and smooth and it keeps the animal calm.
ETA - whenever you're handling sheep you DO need to keep your knees BENT - a sheep coming at you is just about knee high and will take your knees out if you've got them locked, or get caught from the wrong direction.