MB3 97a: Milking Animals on Shabbos (305:20-22)

Milking an animal is a problem of מפרק. Milking onto a food (as opposed to an empty container) is a d'rabbanan. You can have a non-Jew milk your animal on Shabbos since not milking the animal is צער בעלי חיים. The milk is prohibited until after Shabbos since the animal is muktzah. Asking a Non-Jew or Milking with an automated machine on Shabbos.

A non-Jew riding your animal on Shabbos to bring it to water.