Place all of your fingertips together and put a thin sandwich bag over them. Now spread the fingers apart about 2" and press the middle of the bag down towards the palm of your hand, creating a "cup" for the milk to go.
I have never milked a cow in my life, but I have a feeling it is relatively similar though on a miniature scale. Alpacas have surprisingly small teets, especially compared to my distant observations of sheep and cattle. The teets are about 1/2" with a relatively small utter.
With another person holding the alpaca, place your bag covered hand over one of the teets. Reaching up to the base of the teet, perhaps 1/2" from the sides, squeeze the milk down from the top, through the teet and into the bag. Do this several times and the move to the next teet, rotating around all four. You will likely find that some teets are better producers than others.
Oftentimes you will only get about a quarter cup or so of milk if you are lucky. The mother is NOT going to like this at first. She is stressed about her baby and does not want you under her. If this goes on for several days, I have found mothers that will begin to tolerate this more readily, likely because the pressure the milk creates not having been nursed in a while.
Several important notes - if the baby has never nursed, the first few drops from each teet will be colostrum, necessary to create the crias immune system for the rest of its life. Cria must receive colostrum within the first 12 hours, preferably within the first 3-6 for the best absorption. If you are getting colostrum, get the first few drops from each teet, feed it to the baby, then go for the milk. The colostrum should not be diluted with too much milk in the very first drink of its life.
To get the milk to the cria, suction the milk into a small syringe. If you can get the baby to drink from the syringe, that is ideal. However, often the baby is too weak and you do not want to see any of the little milk you can manage to get drip down the side of its mouth. Thus, a feeding tube must be used.
Do this very carefully. Get a feeding tube, place one end of the syringe on it and slowly place it in the cria's mouth. This will cause them to make the swallowing reflex. Push the feeding tube several inches down the neck. Give a very light push to the syringe to make a couple of drops go down the tube. If the cria coughs, the tube is in its lungs. Pushing milk down could cause it to drown. If there is no cough, slowly push the syringe of milk down into its stomach.
HANG ON TO THE FEEDING TUBE! If it comes off of the syringe or you do not hold on while getting additional milk, the baby will swallow the tube...which is a whole other blog.
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