Close curve only closes the curve using the already existing endpoints. If you need to attach two different curves, that would be the attach curve command/tool. If you can get your hands on a "NURBS modelling in Alias" book from the Alias Studio/Poweranimator manual set, it's a pretty good resource that is quite educational on how NURBS work. The books I've seen at technical bookstores go too far in depth unless you want to program graphics. A fairly simple (and very generalized) way of thinking about nurbs is curves that you draw the endpoints of the bezier rather than the point of the curve. Any techies will flame me on that overly simplifies generalization of NURBS, but it's a start. The first few pages of "Using Maya|NURBS Modelling" from the Maya manual set briefly describes NURBS, but I think the Alias Manuals are a much better resource.
Keep in mind that if you want sharp corners in a NURBS curve, 3 CVs will have to be in the same exact location for it to turn sharply, 3 CVs have to be in line for a line to be straight. That is unless you're using linear curves. And before you ask...a curve can not be linear and uniform ("curved"). You'd have to have either two seperate curves or line up and/or snap CVs to give that illusion.
If you're in a hurry to get something from Illustrator to Maya, try using Invigorator and importing as curves. It will automatically import beziers from Illustrator into Maya as NURBS curves. Works quite well too. Your school may or may not have installed it, Maya ships with a "light" version of the plug-in.