Ok, Remember the recruiters?? After you choose your side (or choose to stay neutral). Talk with the recruiter again, and you will have the option to ask how to get to the mainland, he will then give you an access card. 

Now, go up the ramp that is behind the recruiters, and inside a door, there you will find the whompas (teleporters). Here is a picture of the whompa room. In front of each whompa is a computer, pick up your access card, and right click on it. (you pick it up by left clicking on it.)

So there we are, happy adventures in Rubi-Ka!