The trick is to work out the exact reason why you're afraid of failing.
Often, you'll realize that there is some technical reason you don't want to attempt the task - that is, you just don't have the knowledge or skills required to do it. The answer is to be straight up about it with both yourself and others. Either you have to learn the skill to the point where you can do the task (in which case, you'll find that the task becomes rewarding once you are competent at it, rather than a driver for procrastination), or you have to delegate or abandon the task. Don't just leave it! We all know where that leads - a bad place of bad consequences in your life, and just more stress.
Sometimes, there is nothing physically stopping you from doing the task, but the problem is all in your head. What are you afraid of? Perhaps it's looking like a fool if you fail, being embarrassed. Perhaps you don't want to fail for yourself - you feel like you just can't live with yourself if you fail. Perhaps you have a parent, spouse or co-worker who will censure and criticize you if you fail. Regardless, you have to realistically think to yourself, "What's the worst that can happen?" In 99% of cases, the worst case scenario is some hurt feelings - and even that can be alleviated by teaching yourself to be a little more thick skinned. In any case, it's got to be better to have tried and failed than to not have tried at all - think of that enormous stress you have to carry around when you don't even attempt the thing you're procrastinating about in the first place!
The main lesson to take away is that failure is a natural part of life. Just because you fail once at a particular task doesn't mean that you yourself are a failure. The guy who doesn't try at all is the real loser, who doesn't have the courage to at least try once, and lives his life crippled by his fear and doubt. The guy who tries, fails, then picks himself, learns from his mistakes and tries again until he succeeds is the real winner - that takes real guts! But you'll find that the rewards and the boost to your self esteem far outweigh the pain of any purely temporary setbacks.