With milk, the verb is to do something to something. So to milk a breast is probably ok (but not very common, and most would consider it rude). If you're in a situation where you are "milking" someone else's breast, I would assume that is acceptable too (again though, probably considered rude).
That said, I have often heard the verb milk used in relation to humans when talking about actions focused on machines. For example "That machine milks me better than that other machine." Again, here though, while not "rude" exactly, it's a relatively rare thing to hear or say, and the people doing the saying are generally "comfortable" with what's going on, and using "milk" as a verb is more than likely to reduce stress.
So, that brings us to "what to say". If your looking for something more "clinical" then "express" is your go-to option. But keep in mind that "express" is what the mother is doing. She is "expressing" milk.
If you talking about the baby, then the baby is sucking, feeding, breastfeeding, or nursing.
Usually, if you are talking about a breast pump then, "pumping" is commonly used. Collecting may also be common.
The mother expressed some milk for her child.
The baby nursed at her mother's breasts.
The child was feeding at his mother's breasts.
The mother pumped 4 oz. of milk using the pump for overnight feeding.