The ability to tune a drum well is a very very valuable skill to have as a drummer, someone who knows what they are doing when it comes to tuning can make even the cheapest drum kits sound decent. Especially if you are a performing drummer, being able to tune your kit is extremely important, no matter how good of a player you are, if your drums sound like crap your playing will too.
Reducing bad overtones is a good place to start if you want a drum to sound good, but you don't want the drum to sound dead either. Generally loosening off the bottom head, and not having the top head too tight will get rid of some overtones, also you want to make sure your tension rods are pretty even. Especially when miking up your drums, you want to make sure you aren't producing a whole lot of overtones with your drums. If you are having troubles a good ol' piece of duct tape on the drum can do wonders.
Another important part to tuning a drum is making sure the tension of the skin is consistent the whole way around. This is done by changing the tension of the tension rods. The most common way to do this is to go around the drum using the tensioning pattern*, hitting the drum adjacent to the tension rods around the drum and comparing the pitch of the sound made next to each rod is how to make sure the head is even, if it is, all points of the drum will produce a note of the same pitch. If not adjust the head according to the sound compared to the other parts of the drum until all are even.
Another aspect that comes into account is the heads on your drums. Generally the older/more used the head, the worse is will sound. I find that the older heads tend to go out of tune quicker. A new head sounds better when tuned and stays in tune for longer. As far as heads go two-ply heads are great for naturally dampening the drum, and are my recommendation for batter heads.
It takes a lot of experience to be able to tune a drum efficiently, and it can be very frustrating when you can't get the sound you are after, there are a lot of tools on the market that can make tuning easier. If you are having trouble, the sound tech at a show, your drum teacher or even the salesman at your local music store may have some advice on tuning.
