Solder the ground wires to the new potentiometer.

For the ground wires, begin by melting a bit of solder onto the potentiometer.

Then, with the hand not holding the soldering iron, take the wires and place them into the solder. Keep holding the iron to the solder and wire until the wire is submerged in the solder.

Remove the soldering iron. Keep on holding the wire until the solder solidifies, then you may let go as a connection has been made.

Repeat this with the rest of wires.