"Island" kitchen sink vent
You'll use a 3" x 3" x 1-1/2" PVC DWV Sanitary Tee. It's important that you use a sanitary tee, and that you fit it in the proper orientation.  



Or a 3" x 1-1/2" PVC DWV Reducer Coupling





Venting island fixtures can be difficult, since you obviously can't simply install a vertical vent pipe.  The Family Handyman has a good article on How to Plumb an Island Sink

You'll notice the article provides two methods, either you provide a separate vent line, or you use an air admittance device (AAV). The AAV method is only going to be accepted in some areas, so check with your building department before going that route.



As for which way to install a tee.  If you're installing a straight tee, there's no wrong way.  If you're installing a sanitary tee, you'll have to pay attention to the direction of water flow.

Let's say you have a sanitary tee like this



If the flow is down like this...



You can have water flow in like this...



If you have the tee like this...



It's upside down, and you can't have water flow in like this...