Several years ago we bought our first two goats as weanlings. The next spring, I decided maybe I'd better get a goat that knew how to be milked, since I'd never done this before. It was probably the best decision I ever made. When it came time to milk Dream, one of the original pair we'd bought, it was a one-goat rodeo!
I asked a friend for advice, and what follows is the gist of what she told me, tweaked a bit for my own situation and added to by my experiences.
1. Assume that for the first week or ten days, you are only going to give the milk to the dogs. It will keep you from being upset when the goat sticks a hoof in the bucket, or dumps it all over the milkstand. Really, it will. ~smile~
2. Use a tall stainless steel stockpot to milk into, not a fancy milk bucket. It will be harder for the goat to stick her hoof in it.
3. Have a second pot/bucket. Pour the "good milk" into it every so often. When she sticks her hoof in the bucket, you might already have some in the second bucket that is clean.
4. Attitude is important - YOUR attitude. Assume that today the doe is going to be well-behaved. Relax. Be patient.
5. Always do things in the same order, every day. You are in the business of training animals.
6. Get your doe used to being handled before she ever comes into milk. Of course this isn't always possible, but if you are raising your doe from a weanling or newborn, it will be easiest to raise her to be a milker long before she is one.
7. Measure her feed before letting her in the milkroom. Hopefully she already knows to jump on the stand to be fed. Have everything ready before you start. Lock up the cats or puppies or anything else that will be distracting to her or to you.
Ok... now you're ready. Use a washcloth or paper towel to clean the udder and teats. I've recently begun using squares of flannel cut from old flannel shirts. I use the udder wash solution at http://fiascofarm.com/goats/teatdip-udderwash.html , except I substitute white vinegar for the bleach. Dry the udder with another paper towel. Direct the first couple of squirts into a strip cup (I use a paper cup), then milk into the bucket. After milking, dip the doe's teats in the same udder wash recipe as above.
8. If your goat is especially difficult, you can squeeze her leg with one hand while you milk with the other. Squeezing this tendon will help keep her from kicking.
Get the milk bucket into the kitchen as soon as you can after milking. Strain into jars and immerse in ice water. I put the whole shebang (jar in a pitcher of ice water) into the refrigerator. Enjoy!