In a four way circuit, there is a 4 way switch between two 3 way switches. If you don't know what those are, think of a DPDT switch in between two SPDT switches. I had to make a DPDT switch using relays.
{*} {* *} {*}
{*} {* *} {*}
{*} {* *} {*}
^ ^ ^ ^-switch 3; SPDT
^ ^ ^-switch 2; DPDT
^-switch 1; SPDT
{C} {E E} {E}
{A} {C D} {B}
{D} {F F} {F}
A connects to B when the circuit is closed.
If this doesn't help you here it is with numbers:
{1} {4 4} {4}
{2} {1 3} {6}
{3} {5 5} {5}
I really don't know how else to explain it.
I added in the smaller circuit on the right to demonstrate a 3 way circuit.