Let me start off with conceding that I am a novice with arduino and also fairly new to these forums so I apologize if this question has been asked before.
If you are only installing one or two (front door(s) only), it looks like you only need to connect 3 of the 5 wires.
It looks to me like the actuator itself requires 12 volts, as input on the brown and white wires. That means that you will need a couple of 12 volt relays. The relays will control the 12 volt in to the actuator. The Arduino will trigger the relays. Got any relays?
No personal recommendations. The relays need to be operable by 5 volt, 20mA, and need to handle whatever amperage the 12 volt supply delivers to the actuators.
That is not very likely most relays take more current than you can directly drive with an arduino output. For ways to drive your actuator look at this:-
http://www.thebox.myzen.co.uk/Workshop/Motors_1.html
It talks of motors but applies equally well to actuators.