Generally, I prefer to fish only one fly at a time, as I enjoy getting lost in concentrating on that one fly and how and where it is drifting. There is something about trying to remain in "touch" with that one fly as it drifts through an underwater lie, or maybe along the surface over a feeding fish. That's not to say that I don't fish a two-fly rig when I think it is the best option, and that typically for me is most often in the wintertime.
With nymphs, the usual way to do this is to tie the larger, heavier fly to the end of your leader (this is the point fly). To this fly, a length of tippet, 15-20" or so long, is tied either to the bend or to the hook eye, and a smaller fly is tied to the end of this (this is the dropper fly). Depending on the weight of the point fly and the depth and speed of the water you are fishing, you can place one or more split shot either above the point fly, or below it. When fishing fairly thin, clear water, I will often go with two small flies, my point fly being what I think is the heavier of the two. For instance, I'll use a pumpkin head midge or weighted scud for my point fly, and the dropper fly will be a smaller zebra midge or caddis larva.
The key to fishing this or any other nymph set up, is getting the the proper amount of weight (flies and/or split shot together) to maintain a drag-free, down near the bottom, drift. My goal when fishing nymphs is to keep as close contact as possible with the flies without imparting any unnatural movement. I don't use a strike indicator to do this, but if that's how you normally fish nymphs, by all means fish the rig that way. Do what works for you.
Here's a couple of larger point flies - a weighted Vinnie's Isonychia nymph, and a Bead head Bird's Nest.
Here's a few smaller nymphs I like to use in the winter months, along with a favorite midge dry - the three nymphs clockwise from top: #18 Bead head Bird's Nest; #18 Chimarra caddis larva; and a Pumpkin Head Midge. The two dries are #18 Mathew's Zelon Midge.
The Zelon midge is a great winter midge pattern that also works at other times of the year when small flies are the ticket to catching trout. Sometimes a double rig using a Griffith's Gnat and a Zelon midge covers a midge hatch with great results.
And sharpen those hooks, you never know when the big one is going to take your fly.