Once you've removed the tick, drop it into a small jar of alcohol. This will kill the tick and preserve it for further examination, if that proves to be necessary. Carefully swab the area of your pet's skin around the bite with alcohol to kill any bacteria that may be left behind. Finally, jot down the date and time you found and removed the tick, where your animal may have picked up the tick, and where on your animal the tick was attached. 

If You Leave Some Behind... 
If you do break off part of the tick's head, you will see small dark spots under your pet's skin where the tick was. You can try to tease the remaining pieces out if your pet is especially mellow, but it's best to leave them alone. The area will form a small pimple and then fall off. If your pet is very uncomfortable, though, take him to the veterinarian to have the area attended to. 

Keep in mind that many of the pathogens that can infect your pet can infect you, too. You should wear gloves when you remove the tick -- especially if you need to handle the tick. After you've performed the removal, always wash your hands thoroughly. 

A Stupid Pet Owner Trick 
One word of advice-never, never use the old folk remedy of applying heat (such as a match head or a cigarette) to a tick to get it to release. Researchers have found that ticks so treated will frequently "spit up" before they release, thereby transferring any pathogens they may be carrying into the host. The whole purpose of removing the tick is to prevent this from happening, so don't use heat under any circumstances. It's better to leave the tick where it is for a short while until you can remove the tick properly.