A stabilizer does just what it says. Stabilizes the bow---keeps it from moving so much when you release. That's why a short one (less than about 7") isn't worth spending the money. They also absorb vibration from the bow, reducing noise and "felt" recoil. The longer the stabilizer the more effective it is. Note that Olympic and target archers often use one that is as long as 42". If you're looking at a hunting setup then that obviously is too long. 7" to 12" is the norm for best results.

Tuning has been mentioned and you'll get to this, with some help.
Form is what you really need to work on. Try to get some coaching to "Not" point out your flaws but show you what to do right. Then once you learn some good stuff you want to repeat it, shot, after shot, after shot. That is the secret to shooting groups. No matter whether you are having a good day or a bad day, shoot form. Forget score.

Whether your bow is tuned properly or not, if you do the same thing on every shot then the arrows will group together. Tuning helps make the bow more forgiving of shoot form flaws. There is more to it than this but this touches the basics.

Your grip on the bow is VERY important. Try this. www.bowsite.com. Click on features, practical bowhunter, grip (dated Sept 1999, I think). This is a good read with pictures to show you how to NOT grip a bow. By that I mean that you should not grip a bow. You should let it sit in your hand. Read this and you'll see what I mean.