The most difficult part of the wheelie for the bike is to get the front tire to break contact with the pavement. This is where the clutch comes in handy. By bumping the clutch as you twist the throttle, it gives your bike that little extra help to get the front wheel started. Once it's two inches up, the rest is all throttle control. As the front comes up, begin to close the throttle slightly. The front will slow in it's assent towards the heavens. I like shifting to the next gear before I reach the BP. This makes the front more manageable once you are balanced. A higher gear let's you do sustained wheelies a lower RPM. It takes much practice to get brave enough to bring it all the way to balance. You will swear you are going on your backside long before you actually reach balance. I find not to many guys are willing to put in the time on one wheel to get comfy riding the BP? But once you have achieved this skill level, it's such a rush!
The side to side movement you get when you are up is most likely due to an over inflated tire. You won't get this side to side wobble until you get up pretty high. As long as the front is low with the bike under accelleration, there seems to be no side to side movement. Believe it or not, the faster you go, the easier it is to wheelie. Sustaining a wheelie at 60 mph is much harder than at 120 mph.
You don't have to crash to learn how to wheelie. Just take it in little baby steps. Learn to wheelie a foot high, then two feet and so on. Make sure you feel quite comfy doing a one foot wheelie before you move to a two footer. Then, start going for distance. First try doing a 100 footer then 125 etc. Pretty soon you'll be on one wheel for miles not feet.
The way I do a clutch wheelie (Start in low gear if you are inexperienced) is to begin with a rolling start. Once you are moving apply the throttle fairly aggressively, maybe half throttle. As the tach comes up through about 5K just bump the clutch with one or two fingers and increase the throttle at the same time. Not wide open but just slightly more than you have. If the front don't break contact, try it again and give it just slightly more throttle when you bump the clutch than you did the previous try. Soon you'll find that sweet spot on the throttle that works just perfect.
My suggestions to an inexperienced wheelie guy, is to learn to get the front up with throttle alone in low gear before working with the clutch. Master low gear throttle wheelies before moving up. If you are trying to learn how to get her up, the clutch just adds one more thing to think about. Keep it as simple as possible in the beginning.
I remember my first clutch wheelies. My fear was the bike would just flip violently over backwards and send me to the ER? That's not the case as all. As long as you start with little baby steps and don't over step your skill level at any one time, it's a fun process while learning.
Remember, Wheelies are against the law in every state. Make sure you practice in some desolate place where LEO seldom treads?