Do you find yourself playing Mom to someone else's "kids?" Here's how to get those rambunctious baby goats off to a healthy, well-fed start.

The kids waiting eagerly for their next meal.

[edit] Steps

Prepare the milk. This might be cow's milk (although it is best to try to avoid it because its fat content is much higher then goat's milk, and it's not as good for the babies), goat's milk from a CAE-free lactating doe (see Tips and External Links), or a prepared formula.
Prepare two empty, 20-oz. bottles to be filled by putting a funnel at the top.
Pour the milk into each bottle, through the funnel, until the bottle is full.
Attach the nipples to the top of each bottle.
Offer one bottle to each kid, holding it at the level at which the doe's teats would be available.

The kid is likely to take breaks from suckling about every 20 seconds or so, probably to release the suction in the bottle. Some nipples have a small tab on one side of the base, and you can hold this with your index finger while pushing the opposite side of the base most of the way up the threads of the bottle with your thumb. When done properly, you can see air bubbles rising as they enter the bottle. This helps to vent the bottle and reduce suction.

You can feed the kids a specified amount (around 1-2 bottles each,or whatever is recommended on the formula package) or until they are full and lose interest.
Wipe the milk off of their faces and fur. If not, they might lick spoiled milk off each other later.
Make sure the kids have someplace warm and draft-free to lay down and digest their meal.
Clean everything with soap and water for next time!

[edit] Tips

Bottlefeed your kids 2 to 3 times a day, at even intervals.
It's common management practice on dairy goat farms for the kids to be separated from the mother goat (the "doe") immediately following birth. This is because there's a virus that can be transmitted through the milk that causes arthritis later on in the goat's life. See the "External Links" for more information.
While it may make you feel all warm and fuzzy inside, it's generally not a good idea to have the kid(s) sit or stand on your lap while bottlefeeding. As they get heavier, this will become cumbersome and inconvenient. The very act of bottlefeeding will socialize the kids to humans; holding them close while doing so is not really necessary for this purpose.

Some commercial formulas, such as Purina Kid Milk Replacer, have directions to avoid overfeeding. Overfeeding of these formulas can cause scours.
Avoid taming and becoming attached to commercial meat kids to the point that you cannot bear the thought of them eventually going to market.