Have you ever sighted your scope in? I.e. go to a range and fire three shot groups to make sure you're actually hitting where the cross hairs are pointing? If not, then you're not just "kind of beginning", and that IS your problem.

If that isn't your problem, make sure you're not getting shadowed...if you shift your eye side to side in the scope you will see a shadow, similar to shadows on the moon, if you shoot with a shadow, you're not actually "aiming" at what the cross hairs are on...I forget at the moment which direction the shot moves relative to the shadow, I believe it is away from the shadow, i.e. if your shadow is on the right side, you're going to shoot left of your aiming point.

Or it could be that you've got a BSA scope that isn't worth much. Have you tried hunting without it? just using the open sights?