Goats are intelligent animals -- sometimes too smart for their own good. If they decide you're trying to catch them for reasons they won't like, they won't come to you, period. While a timid and semi-wild goat will never become entirely tractable, there are a some things that can help you tame that skittish behavior and bring your suspicious goat close enough to handle.
First Things First
Start things out on the right foot at the beginning -- that is, from birth. If you handle your goats often and with gentleness, they'll learn to trust you. That's important because a goat that doesn't trust your motives will not come to you. Chasing them around to trim hooves or give shots is enough to try the patience of a saint, and makes even the most laid-back goat owner wonder why they ever thought keeping goats was a good idea -- taking time to build trust from the start is well worth the effort. Yelling at goats only scares them, and you should never, ever strike a goat for any reason. Quiet, gentle persuasion and positive reinforcement work where negative and scary behavior fails.
Reinforcing Good Behavior
OK, we're talking about bribery here, but goats won't mind a bit of corruption for a good cause. Carry a pocketful of goat treats at all times -- small pieces of dried apple, oatmeal cookie, raisins or corn chips are good -- so that when a goat comes up to you voluntarily and allows you to touch her without running away, she gets a treat. Don't attempt to hold her or do anything with her at this point, merely offer the treat and continue whatever you were doing. Soon your goats will begin seeing you as a mobile treat dispenser and begin following you around whenever you enter their yard. Once this behavior is consistent, up the ante by gently holding a goat for a minute or two before offering the treat. Keep at this until every goat allows you to examine her mouth and hooves or otherwise handle her without becoming upset. When the behavior is consistent, begin withholding treats occasionally so the goats learn not to expect a treat each time.
Neutered male goats -- called wethers -- never develop sexually, and so retain many of the innocent baby behaviors of kids. Because kids are more trusting than adults, retaining those characteristics is a big step forward in having a goat that will come when called and remain loyal, affectionate and sweet-tempered. If you already have goats, you don't need to be told that your wethers are generally the most affectionate and docile members of the herd.
Train to Grain
One reliable way to attract goats is to train them to come when you feed their grain ration. Use the same bucket and try to feed at the same time each day. Almost all goats love grain, so the minute they hear the tell-tale sound of the scoop in the grain bin, they'll come running. If they routinely do this, using grain to entice a goat at other times -- when milking, for medicating or examination -- becomes easier. Keep track of the amount of grain offered and include that in the daily allowance to avoid over-feeding.
Only pregnant and nursing mothers benefit from a regular grain ration. Grain is not necessary for healthy males or immature goats of either sex, so it's important not to give too much.
Keep Them Curious
When all else fails, you can always appeal to a goat's innate sense of curiosity. Goats are nosey. They poke their noses between hammers and nails to see what you are doing. They peek over fences. They taste everything that looks interesting -- in case it turns out to be edible. You can use their natural curiosity to your advantage by engaging in some activity they don't understand -- preferably inside the stall or isolation area in which you want to confine them. Sooner or later, they'll come to see what you're doing, and you can reward them with a treat -- just before you shut the gate behind them.