How are ions 'pumped' across a membrane during electron transport?
Short answer:
Electrons flow through membranes by floating through kind of channels made out of iron-sulfur clusters.

Long answer:
Let's take a look at the electron transport chain in the inner mitochodrial membrane. There is a proton gradient across the membrane building up a potential difference by pumping protons across the membrane as electeons flow through the respiratory chain. They (electrons) like to flow throught the respiratory chain because they can go from enzyme to enzyme each with a lower standart free energy. These enymes together form one big complex within the inner membrane with Fe-S clusters enabeling electrons to flow through the membrane by giving them a kind of a power stroke (see here).
This as an simplyfied answer on a example.