From the National Pygmy Goat Association, but the info applies to all goats. 

Goats need their hooves trimmed. How often will depend on space, diet, climate, soil, and moisture levels. Where we are our goats are on 5 sandy acres and it's very arid, so we only need to trim hooves about every 2 months for maintenance. In the past we have lived in areas with lush grasses and ample rain fall during which time we needed to trim hooves about every 4-6 weeks. Pick up your goat's feet and look for excess growth to determine if they need a trim. 

Trimming is very easy once you've got the hang of it. First, you'll need a good pair of shears. Garden shears or hoofrot shears work, even a pair of good scissors would to the trick. These are my favorite for my herd because the blades are narrow enough to get to their small toes. 

It's a good idea to leash your goat somewhere safe or use a stanchion to hold your goat while you work on their feet. If you take the time from a young age to work with your goat's feet trimming is easier, much like a dog. However, if you haven't worked with their feet or they're just particularly stubborn they may pull away or try to kick free. Hold your ground, hang onto their foot until they settle, and remember not to cause any injury -- an injury will just make them even less cooperative the next time! 

In case you do draw blood, have blood stop powder on hand! The above illustration recommends iodine but this will not stop bleeding, blood stop powder is a better option.

Clear away any dirt or debris from their hooves to prevent from dulling your trimmers. Trim the side walls until you see white inner walls. Trim their heel only to remove the callus and make a flat, balanced foot but leave plenty of their heel pad to walk on. Their heel should still be white or very light pink, once you see pink you're getting close to blood. And finally, shorten the toe. The toe is the are you are most likely to draw blood if you cut too short, so take off very thin sections of the toe at a time until you're happy with the length. You'll know you've done a good job when your goat's feet set straight on the ground with their toe not quite touching the ground (look at your tennis shoes, the toes don't touch the ground until you walk forward. Same idea with trimming goat feet!)