Your user manual says you can use an opto-coupler but they don't really give you enough information... I'd go-ahead and five it a try and worst case it won't work and maybe you fry an opto-coupler.
[u]This page[/u] shows an opto-coupler driving an LED.
This is a bit of a guess but in your circuit you'd connect the emitter (pin-4) to the common connection and the collector (pin-5) to the switched connections. (I'm assuming there is already a pull-up resistor.)
And of course, you need the resistor on the input (in series with the internal LED).
Since you need 3 "switches". You'd need 3 opto-couplers or a quad opto-coupler. (Of course the pin numbers will be different with a quad opto.)
The most foolproof solution would be 3 relays because a regular 'ol electro-mechanical relay* is an electrically operated and electrically-isolated switch. (You need a driver circuit to drive a relay coil from the Arduino or you can get a relay board with a built-in driver.)
- I would NOT use a solid state relay in an unknown circuit. Solid state relays are finicky about AC or DC, DC polarity, and voltage.