Side-hill, down-hill and up-hill lies are not as difficult as every makes them out to be. I find one of the biggest mistakes made is that people do not take a practice swing before stepping up and hitting the ball. In order to maintain your balance it is important to feel the lay of the ground with the correct stance. You always want to swing with the terrain keeping your shoulders and hips level to the ground and trying to swing through all your shots as much as possible. During the practice swing you also need to observe where the club head brushes the ground as this will be the point of impact with the ball and you should take your stance accordingly.
Side-Hill (above the feet)
When the ball positioned above the feet the ball will be closer to you. Depending on the severity of the hill you will need to choke down on the club. The feel will be that you are swinging around more as again you are swinging with the terrain. It is easy to hook the ball from this position as you arms take over. But if you are able to complete a good follow through the ball will go straight. Compensating for the hook in your set-up is an individual decision depending on what you feel in your practice swing.
Side-Hill (below the feet)
When the ball is positioned below your feet the ball will be farther from you. Use the entire length of the club and depending on the severity of the hill you may need to bend your knees more to get the right distance from the ball. The practice swing will tell you how much to flex your knees as you need to brush the grass with the practice swing. The tendency is for the ball to slice from this position as getting through the shot becomes even more difficult. The slice is a result of contacting the ball with an open club face. However, if you do get through the shot the ball will go straight. Again, compensating for the slice in you set-up is an individual decision depending on what you feel in your practice swing.
When the ball is positioned on a downhill lie you have lost the loft in your club. It is imperative to swing the club down the hill with the terrain so as not to top the ball allowing the club to get under the ball. You may decide to use a more lofted club. Your back leg will be more flexed and how much depends on the severity of the hill. The ball position will be closer to the back foot and how far will be determined when you make your practice swing and see where the club brushes the ground. This is one of the harder shots in golf as the ball always comes out lower.
When the ball is positioned on an uphill lie you can use this to your advantage. The flight of your ball will be higher as there added loft created by the hill. If you have a distance to go and a good lie, you can use a less lofted club or even a wood. In this case your forward leg would have more flex. Positioning of the ball in your stance will be determined by the length of the club and severity of the hill. Again take a practice swing for feel and stance. The shoulders and hips should be parallel to the ground when swinging, adjust accordingly.