Sometimes a strongly worded letter from you or your attorney will be enough to remind them of their obligations. If they decide to ignore that your only real course is to sue them, but sometimes simply starting that process can be enough to make them realize you are serious without having to follow it through. Never threaten unless you intend to do it or you lose all credibility. You also need to consider whether your non-compete clause has any legal standing where the other person lives.
Besides what RonBrown said, you need to consider the costs of enforcement versus the benefits. I have often found that after people cool down from their initial reaction to finding someone violating their non-compete agreement, they decide that the person poses no significantly greater threat than any other person who might compete with them. That's obviously not always true, but you do have to stop and think.
During these tough economic times, a No-Compete agreement has a good chance of being overruled. If the person in question has done what they are being accused of for some extended period of time, and has some documentation backing up the claim that they have done the same kind of work (in the same field) prior to working with you, and that is what they have earned a living off of for some time, chances are the no-compete will not stand.
That is absolutely incorrect, economic times has nothing to do with the enforceability of a non-compete. The issue with non-compete agreements, resides on the enforcablity of them. In most instances the non-compete agreements were created to broad or it was found that they inhibited the person to find work. In vary rare cases non compete agreements can stand, generally in cases where the individual has access to high level company secrets and the opportunity to divulge those secrets to the new employer are too high.