Methods:
1. Tie trailing fly to bend of first fly.
Advantages: Quick and easy.
Disadvantages: Line on hook makes you miss more fish on the 1st fly. Think about it, fish has trouble taking that fly without hitting the line first, which pushes away the fly.
2. Tie trailing fly to eye of first fly.
Advantages: Free's up the hook of the leading fly for better hooking ratio.
Disadvantages: I've heard people claim more tangles, and less feel of the trailing fly, but I can't verify, I never used this method.
3. Droppers. Leave a long blood knot tag. Or, just tie a piece of tippet onto the leader at 90 degrees, using a clinch knot. If you do this, it'll slide, so put it between 2 blood knots so it doesn't slide to far.
Advantages: Regarding hooking, it gets line completely out of the way on both nymphs. Supposed to be more realistic, the nymphs interact with one another less and you can get a better dead drift.
Disadvantages: More tangles, but they're usually easy tangles, just the wrap around type. Tedious to tie up streamside.
Personally I like droppers. A few hints, keep the dropper < 4", and the tippet you use on the dropper should be fairly stiff, you'll cut way down on tangles.
The old style of wet fly fishing actually used multiple droppers to hold extra flies and/or shot. They may have 4 or 5 droppers along the leader, some holding flies and some holding just shot, it leaves plenty of room for adjustment. If you snag up on the shot, it slides right off and you don't break your line or lose you're flies.