I have been playing butterfly guard primarily for the past six months or so. It is a total blast to play, one of the most fun guards. Here are my big tips, things I wish people had told me.
Number 1: It should be called the "wrestling guard," not the butterfly guard. I can't emphasize this enough. You do not play it like other guards, laying back, feet forward. You are not pulling your opponent on top of you. You are sitting up, hips back, head forward.
Number 2: It is all about establishing a dominant clinch. That's what the game is all about -- keeping your legs back while fighting for an overhook, underhook, or armdrag. You do not really put your hooks into play unless you have such a dominant clinch established. Your hooks do surprisingly little in fact -- the game is all in fighting for the right clinch, your hooks just come in to finish the job.
Number 3: The hook sweep. Learn it, love it. The foundation for all that is butterfly guard. Key point with the hook sweep is you MUST fall on your side, not your back. Done right, it's almost unstoppable.
Number 4: This guard works because of the alternation between the hook sweep and regular takedowns, the knee tap and ankle pick. Know that you can hit these off any good clinch (i.e., underhook/armdrag/overhook) with ease. If the guy is pulling back, lunge into him with a regular takedown. If he pushes forward, as he usually will, then hook sweep. This dynamic sets up everything. He can't keep his base back, and he can't keep his base forward. Basically he is in a world of difficulty once you get a good clinch.
Basically I keep my hips back and as the guy reaches in to grab my legs, I look to get the armdrag, underhook, or overhook. I keep fighting till I get one of these clinches. If he grips my pants, I break the grip and attack the arm -- he cannot be allowed to control your legs. Then I attack from there, usually with the hook sweep, following with a reverse hook sweep/x-guard.
Have fun! Don't worry about submissions, they are icing on the cake. The game is all about the hook flip, the arm drag, and the reverse hook flip (or x-guard if you want to substitute that for the reverse hook flip).
There are a couple slightly different types of butterfly guard that deviate a bit from this game. The double underhook butterfly guard allows you to roll on your back, and the collar-grip sitting guard consists mostly of collar-dragging and cross-choking your opponent. But that's spreading out -- the absolute core of the game consists of fighting for the underhook and hook sweeping the guy.
Also, butterfly guard is not hard on your knees at all as far as I can tell, and one of its biggest virtues is that it is extremely hard to leglock a butterfly guard player. I don't know why you would hurt your knees playing butterfly guard, unless you were playing it wrong -- pulling the guy on top of you and on top of your knees might do it. Like I say though, the guy's weight shouldn't be on top of you if you do it right. I suppose the double underhook game might put more stress on your knees.