Can anyone tell me the best way to rig my leader for a two-fly setup, ie to put on a dropper off the main tippet? What knot to use, length of each end....how long should the dropper be, ie. longer than the tippet or should the dropper be the shorter piece or does it matter? Should the tippet be stronger than the dropper?

18 inches is about right for a dropper, maybe a little shorter if you are fishing an emerger behind an adult.
I use a turle not to the bend of the dry fly hook.
5x is usually the tippet on my dropper but sometime you have to go to 6x. Also on a river like the Deschutes in OR you can get away with 4x. A lot depends on clarity of the water and how spooky the fish are. The line to my dropper is usually equal to my tippet if not a little smaller.

If the double fly set up is for sub-surface work, the top fly has to be the heavier of the two. If not the lower one will have a tendency to wrap it's leader up over the top fly. (Did that make any sense?)

To increase your hook ups try tieing the dropper leader to the EYE of the first hook. This allows the top hook to hang below the leader as in the letter "J."

fred.... what kind of knot do you use for these? I have always used the turle but i am trying to picture in my head whether or not that is possible with your system? I rarely use nymphs together but i have before and think i had to use clinch knots

Sorry guy, missed your post.

Usually just a couple of 'improved clinch' knots. For building leaders I'll connect the sections with the Surgon/water knot.

Another school of thought suggests the trailing hook be tied with a knot that leaves it 'swing' in an open loop. Not sure if this really helps ... assuming you're using a fairly light 'test leader,' but it does once you get to 8-10# or over.
fae

I put droppers anywhere from 18inches to 4feet off the hook bend when doing a dry\dropper setup.

The length to the dropper depends on the water and type of dropper i'm using.

As said above, if you are fishing an adult midge with a midge emerger that you want right in the surface film or just under, the shorter leader is fine.

In a river, it just depends on the depth of the river - if I want my dropper rolling along the rocks, you need a long enough tippet for the task. With weighted flies, you can get away with a shorter leader because it will tend to hang straight down. With a non-weighted fly, you might go a foot or so longer than the actual depth since it will be hard to keep the fly directly below the dry.

Keep in mind that you have to pick the right kind of dries if you fish weighted nymphs. Definately use floatant. Choppy water may require an even more bouyant fly.

For double nymph and streamer to nymph type setups, I'll go from 18-24 inches. Streamer to nymph - I tie off the hook bend again.

Nymph to nymph you can tie off the hook bend, off the eye, or leave a tag end on the leader to tippet knot, tie your top fly off of that and your bottom fly on the end of the tippet.

Another thing to keep in mind - the shorter the the tippet (between top and bottom fly) the more likely you'll snag fish. If they go for the top, but you miss when you set the hook, the trailing fly can snag them. If this happens more than once, I either put on a longer tippet, or remove the trailing fly (they were going for the top fly anyway...).