This is an important question. Here are some very general guidelines. For a detailed discussion, please see our article here, or our video here.
Expressing or pumping breastmilk is usually prohibited on Shabbat. But in certain circumstances, it can be permitted for an infant who needs the milk to thrive.
In some cases, a woman may be permitted to pump for her own needs (e.g., to relieve engorgement). In that case, she should make the milk unavailable for use, and discard it. For example, she could put some dish soap in the collection bottle before she begins pumping.
Although it seems counterintuitive, the halachically preferable method of pumping on Shabbat or Yom Tov is to use an electric pump set on a timer or operated with a grama switch. The breast should be positioned on the pump before it starts operating. This is a lower level prohibition than using a manual pump or expressing by hand.
An electric pump should not be left on for all of Shabbat. In addition to ruining the motor, this increases the halachic difficulties because putting the breast on the pump starts the pumping process directly.
Please get back to us with any further questions.