I did this over the last year, having never worked on anything RC before that, so I got a good crash course (literally, right?) in what's in a multicopter. Luckily there are a lot of places to find information.
Polygon and Earthbound have listed the bits that you need quite nicely. My problem starting out was that I didn't know what each of those pieces were. I found a build on Instructables from TogleFritz that is absolutely excellent - one of the best write-ups that there is.
http://www.instructables.com/id/A-SK450 ... -Your-Own/
Use a how-to like that as your guide and you'll be ok.
Basically the motors, prop adapters, and props go together as you'd expect.
The other electronics are built around the flight controller. The radio receiver feeds it your controls from the radio, and it send out "instructions" to the ESC's (electronic speed controllers) that power the motors.
There's also power distribution, straight from the battery to the ESC's, and through a "BEC" (battery elimination circuit) that steps the voltage down to power the flight controller and radio receiver.
At a high level, that's all there is to it. Each piece has its intricacies and pitfalls, but there are idiots that accidentally get this right every day, so you'll be completely fine!
It's not nearly as good of a write-up as TogleFritz has done, but here's my own build.
http://www.instructables.com/id/3D-Prin ... uadCopter/