According to our city law a licensed plumber has to plumb all new construction. I had a plumber put the plumbing under the sink, however I was going to hook up the pipes myself. I am not sure how I need to connect the vent pipe. Can you help me with this?

Your probably better off going to your local hardware store where they can help explain it with the pipes and fittings you will ultimately have to purchase from them. That being said check out the diagram at this website where they are discussing a clogged drain. You can see the vent is inside the wall.
Clogged drain (http://www.plumbinglessons.com/sup/cloggeddrain.htm)

According to our city law a licensed plumber has to plumb all new construction. I had a plumber put the plumbing under the sink, however I was going to hook up the pipes myself. I am not sure how I need to connect the vent pipe. Can you help me with this?

If I understand the question what you have is a pipe coming out of the wall,(the stub out) and you wish to connect the lavatory yourself, yes? Let me know. Tom

What pipe do you think is a vent pipe? Please tell us or describe.