First of all you find a goat :). In my case they have been goats at friends' farms in Keldudalur, Skagafjörður in N- Iceland and at Háafell, Hvítársíða in W-Iceland. The method I have used is a simple one. Catch the goat. Put a collar around it's neck and tether it to a pole or something similar. Sit down either on a stool or on the floor. It is important that the floor where they goat is standing is clean and preferably without any hay or straw.
I begin with combing the neck as most of the goats like that and if they are not ready to be groomed this is a way to get them to understand the divinity of the combing. Then one continues further back to the flank and the hindquarter. Some goats don't like to be combed at the hindquarters and might argue.
The best position for the comber is to have the goat standing on a platform, built for the purpose of combing goats, and preferably be two persons and comb the goat from both sides at once.
I found videos on YouTube that demonstrate how to comb cashmere goats, several videos but here is one
In this link you can see a picture in Lesley Prior's blog where she is combing one of her goats and she also explains the procedure. I am a mere amateur in the cashmere field compared to her.