Pool cues need to be in the best shape possible if you're going to be solid in your game. If the ferrule is broken or split, it will affect your shots dramatically.
Keep the ferrule as clean as possible. As you use it, dirt, chalk and other substances will build up on it. Clean it by wiping it down with a wet cloth and drying it thoroughly. This will extend the life span of the pool cue and improve your game.
Replace the ferrule if there is a split down the side and a tenon running right through the center of it.
Use a lathe or a pair of pliers to remove the ferrule. Squeeze the split on the opposite side and move it around to remove it. Just be careful not to damage the wooden tenon in the middle of the cue stick. If you twist too hard, you might twist off the tenon, too.
Find a replacement ferrule that fits the same way as your broken one. This can be hard because some ferrules are threaded and some aren't. Also, some pool stick tenons are thick, some are thinner. Look online for a match.
Realize that if the shaft has been sanded frequently over time, you may not be able to get a ferrule that fits it perfectly.
Glue an oversize ferrule into place. Turn it down with a lathe or an old fashioned ferrule turning machine until it's the exact right diameter.
Find a good pool cue repair person in your area. They usually charge less than $30 to replace a ferrule. That's much better than attempting it yourself and spending $200 for a new shaft.