How does the fuel pump work in a PA-28 and when should I use it?
The PA-28 Family of aircraft have two fuel pumps, an engine driven mechanical pump that is always pumping (so long as the crank shaft is spinning) and is considered the &quot;main pump&quot;. The airframe also has an electrical backup pump that can be actuated by the pilot. The tanks do not have their own pumps.
You should check the POH for your airframe but generally speaking in the Archer and Arrow I fly the electric fuel pump is turned on:

checking fuel pressure before start
during take off
climb out
when switching tanks (I also run it for 30 seconds after switching tanks incase I either need to switch back and to maintain fuel pressure at a critical time in the event of a failure of the mechanical pump)
on approach
landing/go-around
in the event of a mechanical pump failure
while practicing maneuvers (S-Turns, turns around a point ETC)
during a practice stall
Engine power loss in flight
Loss of fuel pressure

Most of the above items can be found in this POH.
Note: You should not be running the electric fuel pump for the entire flight, like anything this is a component that can burn out and it should be used when needed or dictated by the POH.