relays and switches are easy.
The way a relay works is you connect your osmolator's 9VDC + and - to the two "throw" terminals (the top two terminals in the picture). What that means is your 9VDC current (when on) will "throw" the switch, or turn the switch inside the relay on and then power your AC pump.
There will be another 4 terminals that you connect your AC power and pump to.
I'll explain using the picture above where you would connect all the wires:
if you look at that picture you'd hook your 9VDC the "top" two terminals of that relay.
Your AC power wire (from the wall) has two wires, and your AC powered pump has two wires. Notice on the bottom of the relay there are two sets of terminals.
You connect one AC Wall wire to a the top pole on the left-handed set, and the other AC Wall wire to the top pole on the right handed set. You then Connect one pump wire to the bottom pole on the left handed set, and the other pump wire to the bottom pole of the right-handed set.
So then everything would work as follows:
your osmolator switch reads a low water level. It sends 9VDC through it's +/- wires to power the 9VDC pump that'd normally be there. Instead it hits the relay and your relay then turns on the AC power of the AC pump.
It's pretty wordy the entire thing but it's really not that hard to understand if you have one in your hands to look at.