Common ways to Treat drums.

This way you can gradually adjust the sound of each drum, rather than a hit-or-miss approach. The objective is to tape the drum so that the playing surface is unaffected by the tape. For a snare or tom with a diameter of 14" or less, often two small strips of tape (say, 3" long) are often all that is needed. Try placing them directly opposite each other, but out of the way of the playing surface. Their distance from the rim of the drum affects the tonality and decay of the drum, and is therefore a very personal choice, but about 1" from the rim is a good starting point. It is also possible to tape the resonant head of a drum, but less tape is usually used, unless you just want a "thud"(which you may). Experiment. With experimentation in mind, here is a good tip when using tape: Say you want a 3" piece of tape on the drum head. Cut a 7" piece of tape, and fold it in the following manner: 

_/\_/\_ (forgive the art)

so that each section is 1" long. When it's folded and applied to the drum, you should have a 3" section of tape with two flat "handles" sticking up, like this:

_|_|_

Now if you change your mind about the tape placement, it's easy to grasp by the "handles" and move it around, without having to pry the edge of the tape off the drum head.

O Rings

Next, let's look at O Rings (also called Zero rings, etc.). These are doughnut-shaped rings of mylar that come in various sizes to fit a wide variety of drums, and are available from many manufacturers. They can be very effective in reducing the ring from drums, and can give a snare an often desirable "dry" sound, with more pronounced low end. The only real difference is thickness and width, each of which affects the drum differently. They are quite inexpensive, so you can try a few to see which (if any) work for you. Most salespeople will be glad to show you different ones in the store. You can also make your own out of old drumheads. Just cut out the center and the outside hoop of a used head and there you go. A little experimentation with width is all you need.

Felt

This is an old standby, which is most commonly used on  bass drums and, to a lesser extent, floor toms. Treatment with felt differs from other methods in that you apply the felt before you put on the drum head. With a  bass drum, typically you would lay the drum down so that the side you are Treating is facing up. Lay two felt strips (thickness and width are up to you, but thin and narrow should suffice) across the opening, evenly spaced out, say running from 10 o'clock to 8 o'clock and from 2 o'clock to 4 o'clock. Now, while keeping the felts evenly tensioned (rather tight) across the opening, put the head and hoop on the bass drum, and tighten the lugs until they are all finger-tight. You may need to ask a friend to help you. Among those who advocate drum Treatment, there are two schools of thought on felts. Many feel that, while it works, there are better and easier ways to Treat a  bass drum. Others feel that with the right head, this is the best way to go. As felt is inexpensive, give it a shot. You very well may love it.

Adjustable Pads

I used this term to differentiate between these adjustable mutes (typically felt) and the pads often used in  bass drums (such as those made by DW and Evans). Adjustable pads are often found on older drum kits, and have their advocates today. These are devices where a mechanism on the outside of the drum adjusts a felt mute on the inside of the drum, often touching the bottom of the batter head by various adjustable amounts. These are also found on  bass drums, typically on the resonant head. These pads offer ease of adjustment, even while playing, and can work wonderfully. You should be aware, however, that older adjustable pads that have not been well-maintained may rattle and ring sympathetically. As always, care and diligence can prevent this.

Pillows and Pads

This can be the custom pads mentioned above or an old pillow stuffed in the  bass drum. Foam rubber and towels are often used, too. This approach deadens the  bass drum and changes the perceived pitch of the drum as well.  The amount and effect depend on the method and application, of course. To dangerously generalize, it is often advisable to only lightly touch the batter and resonant head, just to control the decay of the  bass drum, unless you are after a very dead sounding  bass drum (which you may be). Also very broadly, the area of the batter head where the Treatment contacts the head can vary the amount of low end and attack of a  bass drum. It is a good idea to try a towel or a pillow to see if you like this sound (which depends of course on drum size and material, head choice and tuning, beater choice, and, sadly, the drummer). If you find that this sound appeals to you, then look into the products made for this purpose. But you may prefer the sound of an old pillow. A word of caution: don't decide on Treatment based on what you hear while playing. Have a friend play your kit while you listen from various distances. This is always good advice while weighing Treatment options, but is especially important when it comes to  bass drum Treatment.

Control Drum Heads

This includes double ply heads, "control ring" heads, "hydraulic" heads, and good old Pinstripes. While this is addressed in the Drum Head section of the FAQ, please bear in mind that these are Drum Treatments, albeit in disguise. If you like a slight bit of muffling as Treatment in your  bass drum, a "control ring" head may give you the desired result without additional treatment. So if you go from a single ply coated batter head with a pillow to a clear "control ring" batter head, you may no longer need the pillow. Experiment as much as you can, and trust your ears, not an advertisement. While  bass drums are the most common recipients of "control" drum heads, they are also available for toms and snares. 

A Hole in Your Bass Drum Head

Openings (or ports) in a  bass drum resonant head are also forms of Treatment. Even if they are intended only for convenience in mic'ing, they do have a decided effect on the sound of the  bass drum. A closed  bass drum (no opening in the head) tends to have more resonance and sustain. It can have more low end, and particularly a low of low midrange frequencies, which can be an obstacle on stage or in the studio, as the bass drum can fight with the electric bass for room in he mix, even though it may sound phenomenal by itself. For that reason (as  well as mic'ing convenience), very often a  bass drum will have an opening of some sort.  This is less common with smaller  bass drums, such as an 18" diameter drum as is commonly used in Jazz.  The closed  bass drum sound is part of this style, and the smaller drums typically don't fight with the bass instrument as much.

In general, the smaller the opening, the more resonance the drum will have. An opening in the center of the drum may commonly have less low end and more beater attack than an off-center opening. This is a matter of personal choice, and you should listen to both before choosing. The trend in recent years among manufacturers is to put a small (typically 4"-6") off-center opening in their resonant heads. Ten years ago, pre-cut openings were typically larger and more centered. Today there is also a resurgence in closed heads. Again, a matter of personal preference. Be aware that most drum stores will cut a head to your choice of size and placement. You can also do this yourself.

Tip: get a coffee can or other metal  can of an appropriate size, and heat it up  over a stove (please take all necessary precautions so as not to burn yourself). When the can is hot, you can press it against the drum head and a hole the size of the can will quickly be seared into the head. Remove the can quickly and the hole should be smooth. You can purchase reinforcement rings to prevent the edge of the opening from being damaged if you choose, though this is often unnecessary.

Other Approaches
There are many other valid ways to Treat your drums, often with whatever you have handy. Without attempting to list them all, here are two well-known sounds and how they were achieved:

Ringo Starr's distinctive late '60s sound with The Beatles, on recordings Sgt.
Pepper and Strawberry Fields Forever, was achieved (in part) by draping tea-towels on the snare and toms. For those that don't know, a tea-towel is about the same size and thickness as
a dishtowel.

Al Jackson Jr's snare sound on all the classic Stax and Al Green records was often achieved by placing his wallet on the snare.

Tip: if you drop a few cotton balls in toms, they can cut the ring just the right amount without affecting the visual or playability of the toms. When the batter head is struck, the cotton balls lift off the resonant head briefly, then softly and naturally fall back and prevent the resonant head from ringing.