To expand on what streamerguy wrote...
Unless you're fishing a nymph as an emerging bug, you want to get it as close to the bottom as possible (typically).
The lowest portion of a stream is called the "cushion". Due to friction between the moving water and the streambed, this water moves slower than water further up in the water column. Fish use this feature to conserve energy by staying out of the faster flows, and since the naturals are coming from the bottom, this is where your fly should be.
There are exceptions, such as cressbugs and scuds clinging to vegetation, and swimming nymphs migrating to their area of emergence, but getting your nymphs to the bottom is key.
Keep in mind, when you fish with split shot, you're fishing the shot, not the fly. By that, I mean there's likely gonna be slack between your nymph and the split shot. The nymph can be any distance away from the shot that the last bit of tippet between shot and fly allows. Could even be downstream of the shot.
For this reason, you might want to keep the distance between shot and fly fairly short. I often keep this distance from 6-8", and almost never more than 1'.
Think about it. If the fly is drifting downstream of the shot, and a fish takes the nymph, the slack has to be taken up until the shot is affected. Once the shot is affected, you can detect the take (unless you can see the take). This applies to fishing by feel, as well as using some sort of strike indicator.
Fish can spit a fly out really quick, so keeping the distance between shot and fly short gives you a better chance at detecting a strike.
How much weight you add depends on the current speed, depth, and fly design. The shot should tick bottom regularly, and get hung up occasionally too. It's a balancing act - too little weight, and the fly isn't down where it needs to be. Too much weight, and you get hung up every drift. In between lies the answer.
One way to avoid the delay caused by slack between the shot and fly is to use weighted nymphs. While this works well, it can affect the movement of the fly, as compared to the naturals.
Hope I haven't scared you. ;-)