I couldn't seem to get my Handi .223 to shoot any better than 1.5 to 2 inch groups at 100 yards until I did these simple things:

1) I found the ammo it liked (American eagle .223 50 gr. JHP).
2) I moved the front rest to be underneath the receiver as much as possible.
3) I made a conscience effort to follow through on the trigger pull.
4) I used better support at the butt stock.

Now, I am shooting groups that fit within a 1 inch square at 100 yards. Not to bad in my book for a factory rifle/scope combination that cost less than $300.