While most golfers practice on a driving range mat that is completely flat, golf isn't typically played on totally flat ground. Most golf courses have humps and bumps, hills of all kinds, and golfers have to hit shots from downhill, uphill and sidehill lies.
Hitting shots from one of those four lies -- downhill, uphill, sidehill with the ball above your feet and side hill with the ball below your feet -- requires some adjustment in how you stand and set up your swing to be successful.
How to hit golf shots when your ball is on a downhill lie
When your golf ball is sitting on a downhill lie, you have to expect that the ball will have a tendency to go to the right. Most golfers don't prepare for the shot properly, so they are more likely to catch the ball in the earlier portion of the downswing, before the club face can be properly squared. That usually means that the face is still open to the target line and will flare out some to the right for a right-handed player.
However, if you prepare properly, you can play the shot to your target and hit a relatively standard shot.
The first thing to do is to move the ball position back in your stance, toward your back foot. The ball position move is commensurate with the slope of the hill. The more grade to a downhill lie, the more you need to move the ball toward your back foot. This is part of what we can do to combat that we're likely to catch the ball sooner in our downswing.
The second thing to do is to keep our shoulders parallel to the slope of the hill. Typically, from a flat lie, our shoulders are, more or less, parallel to the ground and our weight is pretty evenly distributed between the front side and the trail side. We want to achieve this same kind of parallel to the downslope. That's going to mean the feeling that you're tipping your lead shoulder (the left one for a right-handed player) toward the ground. However, what you're really doing is trying to keep those shoulders more parallel to the slope so that you're more likely to catch the ball flush instead of the ground in the downslope first. You should feel some more weight toward the front side of your swing but not drastically so.
The third thing to do is to keep your lower body from moving in your swing so that it's throwing off your shoulders from being parallel to the downslope. This doesn't mean having a completely quiet lower body, though that would be easier to do with a wedge or short iron in hand. The key is to set your legs as best you can to mirror the setup of your shoulders and swing along that body path.
If you pull off the shot correctly, you're going to hit the ball about how you would normally. It may come out a little lower than usual. If you feel capable of controlling the club face well enough, then you can lay the club face slightly open and aim a little more left of the target to create more loft and send the ball higher in the air. The key, though, is to make good contact with the ball first. After that, judging distance from the kind of contact you make is the next-most important thing. Finally, controlling height and spin is a key for more skilled players.
If you know how to handle hitting shots from different slopes on the golf course, then you can handle practically any approach shot the game will throw at you.