Sizzles are specialized effects cymbals, which provide a long decay time sound for a drummer. While not as popular now, with the advent of power over touch-style drumming, they do provide a unique addition to softer/jazz-style players.
There are two methods for creating a sizzle. The first method requires boring precision holes in the cymbal, typically between one to two inches from the outer edge. Make sure the holes are opposite each other for balance, and bore six to ten holes, depending on the size of the cymbal. Clean off any burrs and soften the edges of the holes with a round file.
You can buy brass rivets from a full-service Zildjian dealer, but most old-school drummers would get brass drum-brake rivets from an auto parts store. If you go with the Zildjians, just follow the directions. If you get the brake rivets, purchase two per drilled hole, and make sure you get two sizes of rivets, such that the smaller rivet will almost fit into the larger rivet. Put the larger rivet into a hole from the top side of the cymbal, and force the smaller rivet in from the bottom. Use a smooth-faced tack hammer for best results. When you have all the rivets installed, you have an effective sizzle cymbal.
The second method is tougher to acquire. Several cymbal manufacturers made a clip-on sizzle setup that you could remove when desired. No modification of the cymbal was required, but I personally thought the sound was better and the decay time was longer with brass rivets. Clip-ons are harder to find.
Some drummers will think you're crazy to drill holes in expensive cymbals, and I agree. If you're going to make a sizzle, use an 18-22 inch ride cymbal that has a deformed bell, a crack, or you can even find a beat-up used one. Sizzles are for effects, and overusing it can annoy your listeners, just like using a gong or Chinese cymbal for every song. Make sure you don't do a Keith Moon-style drum solo with the sizzle, as it can easily produce hole-to-hole radial cracks if hit too hard.
It's tough to describe the sound of a sizzle, so I'll just give you an example. Dig out Psychobabble by the Alan Parsons Project, and give it a listen. You can recognize the sizzle when the Stuart hits it during a small break before the main song kicks in.