How is electrolysis used to extract aluminium?

Yes. This is one of the reasons that aluminium was very rare for most of history - there simply wasn't any way to purify it without electricity. Furthermore, aluminium wasn't really able to go into large-scale production until the capacity to produce large amounts of power existed.

Even now, it's far more efficient to recycle aluminium cans than to make new aluminium, because of the huge quantity of power needed to make new aluminium.

The extraction is done by electrolysis of Aluminum oxide. But first the aluminum oxide must be melted so that electricity can pass through it. Aluminum oxide has a very high melting point (over 2000°C) so it would be expensive to melt it. Instead, it is dissolved in molten cryolite - an aluminum compound with a lower melting point than aluminum oxide.

http://www.chemguide.co.uk/inorganic/extraction/aluminium.html

The electrolytic cell consists of a steel container lined with carbon, which serves as the cathode. Carbon rods are then suspended in the electrolyte and these serve as anodes.

The reaction, which takes place at the cathode is

#Al^(3+)# + 3e- ------> Al

This is a reduction.

The reaction, which takes place at the anode is

2#O^(2-)# ----> #O_2# + 4e-

This is an oxidation.
In order to balance the electrons lost and the electrons gained, we need to multiply the reduction half reaction by four and the oxidation half reaction by three. So, we get

4#Al^(3+)#+ 12e- ------> 4Al

and

6#O^(2-)# -----> 3#O_2# (g) + 12e-

The overall balanced equation for the reaction is

2#Al_2##O_3#(l) ------> 4Al(l) + 3#O_2# (g)

The molten Aluminium collects at the bottom of the cell and it is then tapped off.

nice red and blue color to assist comprehension on this page: http://www.gcsescience.com/ex12.htm