Ball Below Your Feet
Hitting the ball when it's below your feet requires strong thighs. In order to keep your spine angle reasonably tall, you have to bend your knees as much as the slope dictates—and keep them bent at the same angle from start to finish. Spread your feet a little wider than usual and stick your rear end out for ballast.
Even with your knees flexed, your swing plane is likely to be more upright than normal, and that will contribute to the ball curving to the right. So again you must compensate, this time by aligning your body left of the target. Fades don't fly as far as straight shots do, so be sure to take one more club—an eight-iron instead of a nine-iron. You will also lose distance because the more bent over you are, the less you are able to turn your body.
Another consequence of a severely bent-over stance is a tendency to overuse the arms. This often leads to a pull, which can be especially bad from a hanging lie because the ball goes hard left instead of along the left-to-right trajectory you were expecting. To avoid this, focus on swinging easily, no harder than your balance and stance will support, and staying strong with your feet, knees and hips throughout the swing.
From hanging lies, advanced players can try to turn the toe of the clubhead over the heel through impact—that is, release the clubhead early—to minimize the amount of fade they impart to the ball. But as with the previous example, that takes exceptional feel and lots of practice and is usually best left to the pros.
When the ball is on a gentle upslope, you can pretty much make your normal swing, provided you properly adjust your stance. Tilt your torso until your spine is close to perpendicular to the ground, and then swing along the angle of the slope. The trajectory will be higher than usual, and these shots are prone to go left—try as you might to make an aggressive turn through the ball, having so much weight on your right side skews your timing. Your shoulders often stop a little short of where they usually do, and that essentially results in a slight pull.
On a steep upslope, however, it's even harder to make a forward weight shift, and I advise leaning into the hill. Focus on driving the ball hard and low; if you hit down on it, the slope and the backspin will make the ball go plenty high. Keep your left arm soft and fold it in after impact, the way you do when hitting a punch shot into the wind. Swing easy, and use more club to compensate.
Similarly, on gentle downhill lies you want to tilt your spine so it's perpendicular to the ground and then swing with the slope. The ball will fly lower than usual, so take a loftier club—use a seven-iron instead of a six—and think of chasing the ball down the slope with your clubhead. The tendency is to pull up and top the ball or to otherwise quit on the stroke, sending the ball to the right. So really go after it: Stretch that right shoulder down the slope aggressively and try to make a complete follow-through, finishing with your chest facing the target.
The difficulty is keeping your balance. Sometimes a little step forward after impact is unavoidable, but you can brace yourself by shutting your stance, keeping the shoulders square and the downhill foot a bit forward of the uphill one.