Successful Delegation

Get someone else to read this... but seriously.
Be specific... It's easy to give someone a vague assignment ("You take care of publicity") only to find out later that what they understood this to mean is very different from what you intended. People need to know what tasks they're responsible for and what the finished product should look like. Example: "Prepare a press release and send it to the local newspapers, TV and radio one month before the event."
...but don't micromanage. Tell them enough so they understand what's expected of them, but not so much that they have no chance to think for themselves. Leaving the person room to make some independent decisions lets them choose a style of doing things that suits them best. It makes them feel respected and trusted and part of the team. It builds a greater sense of pride and ownership in the project, and it gives them a chance to develop their skills and confidence. They might not do the outstanding job that you think you would have, but it might still be good enough--and the benefits to the person doing it are probably worth the tradeoff. So learn to let go!
Agree on deadlines. Make sure the person understands when they can expect things they need from other people, when their part of the task needs to be done, and how this fits in with the larger timeline for the whole project.
Follow up. Check back with the person you've delegated to, to find out how it's going. Ask if any questions have come up since you last talked. Make sure they have what they need to do the job, and that they're getting the necessary assistance and cooperation from others. Sometimes people are reluctant to admit they didn't understand something, or that they're having trouble. Asking gives them an opening and permission to say so. It's also a way of finding out if someone simply isn't doing the job, before it's too late.
Match assignments with people's skills... Some people write well, but hate to talk on the phone. Some people can schmooze anything out of anybody, while others would rather do anything besides ask for donations. Find out what people are good at, and what they like to do, and make the most of it.
...but don't let people get typecast against their will. People with particular skills (artistic, computer, etc.) often get stuck with the same jobs over and over, because they do them so well. If they like it that way, that may be fine (although you might want to encourage them to stretch a bit and do something unfamiliar once in a while). But they may be more than ready for a change--and someone else may be just waiting for a chance to do "their" job.
Make sure assignments get handed out fairly and realistically. Most groups have at least one workhorse who tends to take on too much--sometimes to the point of exhaustion and burnout. Another problem is the person who gets carried away with the enthusiasm of a moment and volunteers for things, then finds her/himself unable to follow through. Encourage people to take a realistic look at their workload and abilities, and to take on the jobs they can reasonably handle.
Give accurate and honest feedback. People want to know how they're doing, and they deserve your honest opinion. Praise effort and good work, but also let them know where they might have done better. Encourage risk-taking and growth by treating mistakes and less-than-successful efforts as a chance to learn and do better next time.

Delegating Tasks, published by the Campus Activities Center at the University of California, Santa Barbara, who in turn took it from a document published by the Texas Union at the University of Texas at Austin

Antleader Guidelines #A4: Delegate!, published by the Student Activities Office at the University of California, Irvine

Tips for Successful Delegation