For the first couple of days, you may want to offer the goats free-choice baking powder, put a little gatoraide mix in their water, and generally try to keep their digestive systems and electrolytes up and running.
And various reminders so that you have them all in one place when you ask later --
I deworm all non-breeding goats with Valbazen. It is suspected to cause abortion in pregnant animals, so use it with care if you use it on adult females. Dosage is two times the listed sheep dosage.
The "baby food" for my goats is the CFC "Lamb Grower 14-B" (medicated) sweet feed. Once they are about a year old, I switch them over to Goat Maker R (medicated) or Nutri-Goat (not medicated) for the rest of their lives.
They also have a plastic dish (not metal) of Ultralyx Goat Mineral loose mineral mix. Note that this is toxic to sheep due to the copper content.
How do you tell if a goat is sick? It doesn't eat, stands around with its tail hanging horizontal or downward, droops its head, grinds its teeth, or hunches its back. Of course diarrhea is a strong indicator of problems, though you may not know exactly what kind of problem immediately from that specific symptom. It could be anything from "shipping stress" (the bacteria in the rumen is upset) to accidental poisoning (azaleas) to worm load.
Excessive worm load will evidence itself in at least one of three ways - diarrhea, a swelling of the jaw and drooping of skin under the chest in between the front legs, and pale lower eyelid. The pale eyelid test is VERY reliable.
The most awesome internet resource comes from Maryland. For all your parasite questions, visit http://www.sheepandgoat.com/ and if you can't figure it out from there, send Susan Schoenian a note.