Most club golfers have a routine for a flat lie that works reasonably well, built up over years of range balls sat on perfectly level mats. Put the same player on a slope and the routine falls apart within a swing or two, not because the technique has changed but because nobody ever taught them what the ground is doing to the club they are holding. Uphill and downhill lies are not variations on a normal shot. They are a different shot, with different physics, and treating them as though a good swing will simply sort itself out is how a comfortable par turns into a scrambling bogey.
What the slope actually does to the club
An uphill lie effectively adds loft to whatever club is in your hands. The ground behind the ball rises, the clubface arrives with more loft relative to the horizon than the number stamped on the sole would suggest, and the ball comes out higher and shorter than it would from flat ground. A downhill lie does the opposite. The ground falls away in front of the ball, the effective loft reduces, and the shot flies lower and rolls out further than the club would normally produce. Neither of these effects is subtle on any lie steeper than a gentle rise, and both catch out players who select their club as though they were standing on the practice ground.
The sideways tendency matters just as much. From an uphill lie, the ball tends to drift left of the target line for a right-handed player, because the added loft closes the effective face angle at impact. From a downhill lie, the tendency runs the other way, towards the right, as the reduced loft opens things up. None of this is a flaw in your swing. It is simply what the slope does to a golf club, and the sooner you plan for it rather than fight it, the more often you will finish near the hole rather than short of it, or through the back of the green rather than on it.
Setting up so the slope helps rather than hinders
The single biggest adjustment, on either slope, is getting your shoulders roughly parallel to the ground you are standing on rather than parallel to the horizon. On an uphill lie, that means the back shoulder sits lower than it would on flat ground, which naturally encourages the ball position to move forward in the stance, towards the front foot. On a downhill lie, the front shoulder drops instead, and the ball moves back, towards the rear foot. Fighting this by keeping a level shoulder turn on a sloped lie is the most common way amateurs turn a manageable shot into a thin or a chunk, because the low point of the swing no longer matches the ground beneath the ball.
Club selection should follow the slope rather than the yardage on its own. Take one more club than the distance calls for on an uphill lie, since the added loft and reduced carry both work against you, and accept that the ball will come out softer and land more gently than usual. Take one less club on a downhill lie, since the ball will fly lower and run further once it lands, and resist the urge to help it into the air, which only leads to catching it heavy. Trying to manufacture extra height on a downhill lie by hanging back on the trail foot is the single most reliable way to hit behind the ball, and it is worth saying twice because it is the mistake that recurs most often on courses with real movement in the fairways.
Balance is the part nobody practises
Slopes pull your weight in the direction of the incline, downhill lies forward and uphill lies backward, and a great deal of poor contact on sloped ground comes from players losing the fight against gravity mid-swing rather than from any flaw in their technique. Widening the stance slightly and committing to a shorter, more controlled swing gives you a far better chance of staying balanced through impact than trying to generate full power against a slope that is actively working to tip you over. If you can find even a corner of a practice ground with a rise or fall in it, twenty minutes spent hitting three-quarter shots from both kinds of lie will do more for your scoring on an undulating course than another bucket of balls off a flat mat ever will.