How much do you push on it? Really? You push until the bike's turning like you want.
That's like asking how much do you turn the wheel in a car? How far do you move your leg when you walk? How wide do you open your mouth when you eat? The answer in each case is the amount you need.
You're thinking too much.
The bike goes towards the bar you push. If you're not turning enough, push more. If you're turning too hard, push the other bar to ease up. You're not actually steering except at very low speed. Past walking speed the bike turns by leaning, and the lean is initiated by pushing the bar.
Don't pay attention to how far it's leaning. The lean angle doesn't matter at all! If you're looking through the turn correctly, you can't even tell how far the bike is leaned.
The bike also follows your eyes. You whould be looking through a turn before you even start the turn. The MSF course actually breaks it into four distinct motions: slow; look; turn; gas. the instructor will want to see your head turned before the bike turns. Notice the first step is slow. The start of the turn should be the slowest speed the bike reaches in the turn. Trying to slow down while turning is BAD.
And your eyes will be well ahead of the bike, not down on the road right in front of the bike. When your eyes are on the road in front of the bike, guess where you'll be? well, you've already said where you were, haven't you?
No braking in slow speed u-turns and eights. Speed control is clutch. More clutch friction for speed, less clutch friction for slow. If you're falling, speed up. If you're going wide, slow down. Some guys drag a little rear brake for parking lot stuff, but just drag, not speed control.
Don't stop and then remember to downshift. You should be shifting down as you slow down, and the bike will already be in first when you stop. You shouldn't shift a stopped bike, anyway. (And NEVER shift a bike with the engine not running!)
When you get to the MSF, you'll be amazed how familiar it all sounds if you've read my posts.
And it might not be a bad idea to just put the thing away until you've been to the MSF. I know how lame that sounds, and how hard it would be to do, but you don't want to teach yourself bad habits. Youtube is full of people who "knew" how to ride motorcycles. Learn on the MSF bikes, and if you drop a bike while learning, let it be one of theirs. They take off the mirror and turn signals because they know it's gonna happen.
(BTW, MSF was nealy $250 here in Florida when I did it, so no whining about the fee.)