Goats need a good shelter. If babies are coming, keep a light on in the barn--a heat lamp is best if labor is eminent. They hate to get wet. They also need a good fence or they'll wander. If you have Nigerian Dwarf goats, you'll need (at least) a 4" woven wire fence--and even that won't keep in the babies. Finally, be a responsible goat owner/breeder. Be aware that sibling bucklings and doelings will breed at a very young age with each other. Wether bucklings you're not going to either sell or keep for breeding. You'll need to separate intact bucklings from the rest of the herd to prevent inbreeding at around two months of age.
Goats are browsers. They like to walk around and sample the greenery. They don't graze like cattle. Plants up off the ground are best because worms and parasites are down closer to the ground, thus more easily picked up. Offer good hay (no alfalfa for your males--look up urinary calculi). Grain should contains Decoquinate to help prevent Coccidiosis as well as ammonium chloride (for males) to reduce the risk of urinary calculi. Always keep loose mineral available (also a bit of baking soda to help with upset tummies is nice). They need lots of fresh water and won't drink it dirty.
Goats love to play and are very curious. Have something they can climb on or get under. Pinterest has lots of ideas for building goat play areas. If you want your goats to be friendly, spend time with them. Let them get to know you. Feed them from your hand, scratch the tops of their heads. Some goats will even enjoy reclining on your lap. Tail wagging is a sure sign your goats are happy.
NEVER have only one goat, as they are very social and need other goats. Goats left alone will be terribly unhappy and may try to wander in search of company. The herd will develop a "pecking order" with a herd queen at the top (see the great article below at Better Hens and Gardens). Herd members may challenge the queen or others higher up by head butting and other seemingly acts of aggression. Take your lawnchair out and just sit and watch the goats. You'll soon learn their personalities and they'll get to know you.
Watch the goats for signs of distress or sickness. This includes not wanting to be with the others, not eating or drinking, coughing, or if he/she just doesn't act right. Something's wrong if goats have diarrhea (scours). Don't dither about getting a sick goat to the vet. They're usually pretty easy to care for if they're healthy. Regular CDT vaccinations and worming as needed should be a minimal part of your maintenance routine, as well as hoof trimming (find a good video on Youtube). Be weary of goats purchased at sale barns.
There are tons of great videos and articles online to help with goat care. Additionally, know your local vet just in case. If you suspect your goat is sick, don't wait. Disease and/or illness can kill a goat in a matter of hours. These little goats can easily be carried to the vet in a large kennel if you suspect a problem. Fecal testing can determine many issues. Talk to your vet about what to do.