Try to get a sense of the depth of the water based on the colour. So where you are standing (probably in the margins) the water will be a certain shade of whatever colour the water is (tea in most of yorkshire!).
Use that benchmark to gauge the average depth of fishing lies that you are going to cast to. Then set the length of mono from the dry to the nymph to be ROUGHLY 20 to 30% longer than that (very approximate). So if you are wanting to fish the fly at a depth of around 2 to 2 and a half feet go for somewhere around 3ft of mono from the dry fly to the nymph.
You can then adjust the actual depth that the fly fishes by changing the weight of the point fly (as JeffR already said - you want the nymph to trail behind the dry, not to hang below it). I usually start heavy and work back towards the surface.
The good thing is that when you have got the right weight of fly - the shallow water tends to be faster and the deeper water tends to be slower; so that the combination of depth and pace virtually cancel each other out as you move along the river and you don't have to switch flies all the time.
In areas where you do start to snag the bottom too often - simply reduce the length of the drift (and do - say - 3 mega short drifts along a line that you would normally allow one longer one to run through). Once you get into the more pernickety situation of competition fishing, you will often find that getting the right fly weight to allow you to do tons of really short (say 18") drifts is far more effective than trying "long trotting" drifts that are yards long. This is most likely because the most attractive movement for the fish is the "dead drift but diving for cover" action of the sinking fly or the "sweeping upwards ready to hatch" movement at the lift. With a shorter drift - a greater proportion of the total time in the water is taken up by these two conditions...
You're probably all sick to death of this clip by now but a very simple example of the kinds of water that lend themself to duo fishing and an illustration of leading the dry fly with all of the leader off the water is given here:
Note that the drifts I show as a demo towards the camera are probably a bit too long to be perfect - and that because it is a demontration to a static camera; I stay in the one place far too long (and even virtually repeat the same drift a couple of times). Once you have put one decent drift through a spot, then don't recast to the same place (you might only have to vary the line by six inches either side, but definitely try to make each drift unique).