A lot of information in this node inherits from my more complete gag writeup, ball gag.
A bit gag is a BDSM accessory used to gag a submissive or bottom by placing a rod (A.K.A. a bit) in between the bottom's teeth, thereby holding his or her jaw apart. This simulates a bit and bridle setup used on horses for equestrian goings on. As one may expect, bit gags are very popular with the pony play fetish subculture in the BDSM world, so any pony boy or pony girl that you are likely to see in your day to day life (If your day to day life is more interesting than mine) is likely to be furnished with this type of gag. Bit gags are also very popular among the non-equestrian-fetish crowd due to the open-mouthed nature of the gags and the fact that some people find bit gags to be much more comfortable than other kinds of gags. These gags, however, provide much less sound muffling, and mostly serve as an impediment to jaw movement, which is good for leading a restrained submissive about.
There is a wide variety of bit gags available on the market today. The attachment used to attach the gag to the head is often of the harness sort mentioned in the ball gag node and is almost always leather. Sometimes bit gags are attached using a less expensive strap behind the head, but this is usually done in combination with other head gear such as blinders for pony play, or as a matter of cost and convenience for non-pony play. These sorts of gags often have extra (or extra-large) rings where leads and leashes can be attached for the purpose of guiding a bottom during a scene, or just jerking their chain, as it were.
Common materials for the actual bit portion of the gag are rubber, some manner of wrapped solid such as leather-wrapped wood or metal, latex (distinguished from harder types of rubber), and rope for impromptu gags. It is possible to tie a length of rope into a gag that looks like a bit gag. I've done it. You can learn how to from a url at the end of this writeup!
Care for a bit gag depends on what it's made from. My usual standard of hot water with a little dish detergent seems to work ok for me, but I don't know what the rest of the world does. Leather is usually unhappy if it gets wet, though I maintain that this is not critical as cows don't leak. Rubbing alcohol is usually your friend, too. If you happen to have a bit gag made from metal or some other sturdy material, you may want to try a bleach water solution to sterilize it.
Bit gags are very easy to make yourself out of a leather strap and an appropriately-sized wooden dowel. If you're looking for an easy way to get into things, a cheap strap of some sort and a homemade gag may do well for you. Of course, the cheapest way to shut someone up is the tape gag, but you only get to use it once. Alternately, you can spend anywhere from $20 to $100 or more for one of these online. A good one will last a lifetime (Unless it's made of latex)!
How to tie a rope bit gag (Checked 1/8/2004): http://www.rainbowrope.com/howto/rope_bit_gag.html