The barnaby flyer paper aeroplane was named after Capt. Ralph S. Barnaby (USN Ret.) (naturally). Paper aeroplanes are very cool and impressive, so impressive that there are international paper aeroplane flying contests.
The most poplular kind of paper aeroplane is the simple dart, practially everyone knows how to make these and they are probably the most simplest to launch and fine tune.
Step 1: Choose your construction material.
I would recommend strong paper with a decent thickness, the A4 printer paper in your office (if you work in one) is ideal, as it is the makings of small and sturdy paper aeroplanes that can do crazy stunts when launched and tuned properly.
Note: I tried using A3 size paper and they do not fly as well, the reason for this is if you consider the rc aeroplanes people fly can do much better stunts than their full size brothers, I cannot fully remember why this is but I presume it has to do with aerodynamics.