I'm about to start my final year project which requires me to develop the Kinect Fusion Algorithm. I was told to code in C++ and use the OpenNI API.
Problem:
First of all, if you're planning to use OpenNI with Kinect, I advise you not to use version 2.0, which is available at the official website. The reason is simply that there currently is no driver yet to support the Microsoft Kinect (the company behind OpenNI - PrimeSense - only supports a driver for their own sensor, which is different from the Kinect, and the community hasn't gotten round to writing a Kinect driver yet).
Instead grab the package from the simple-openni project's downloads page - it contains everything to get you going: libraries from the 1.5.x line.
Mind you that these drivers don't provide a way to control the Kinect's tilt motor and the LED light. You may need to use libfreenect for that.
As for getting started, both the OpenNI and NITE packages contain source code samples for simple demos of the technology. It's a good idea to start with one and modify it to suit your needs. That's what I've done to get my own project - controlling Google Chrome with Kinect - working.
As for learning C++, there are tons of materials out there. I recommend the book "Thinking in C++" by Bruce Eckel, if you're a technical person.