I am interested in learning about arduino. What is the quickest and cheapest way to find out if this is something I can and want to do?
By an Arduino starter kit and do all the projects. There are components and instructions for 15 different circuits. This is not cheap, but I think it will give you a good taste for electronics.
The starter kit would get you everything you need to do a whole set of projects. Alternatively there is a PDF on the Arduino site with a whole set of projects in it. You could go through it, put together an inventory of the parts you need, and order those parts from an electronics supplier like Mouser, DigiKey, Jameco, etc, and save some money.
The starter kit is probably worth the extra money, though, because it has everything you need, plus an organized set of lessons that teach you the various skills you'll need.