A relay is just a switch. Two of the contacts will go in series with your power supply and pump and switch the pump on and off. The other two contacts will power the coil that turns the relay switch on and off, and those will hook up to your breakout board.
The datasheet for your relay (check the manufacturer's website) will show you which pin is which. The application notes for your breakout board should show you how to wire a relay.
You should have a normally open relay for this project, or a DPST relay that has both normally open and normally closed contacts. Normally open means that the switch by default is not connected (if it were the other way around the pump would run when your breakout board was unpowered).