1. I am not an electrician, but I have worked on my own air conditioning units many times in the past.
2. There are many parts that can go bad that cause the fan not to run. For example, you might have a bad switch, or a sensor, or a component with cicuitry, or (if a newer unit) a compterized control panel.
3. The quickest way to test is to use an multimeter. These can be purchased at any hardware store, and they range from the cheap (%15-$20) to the expensive ($100 or more) depending on the features and the quality of the device. An A/C will come with an instruction manual, but the device is fairly simple.
4. Now the tough question: if you do not know what you are doing, why are you wasting time? You might injure or kill yourself, and you might make the problem worse. If this was a $15 box fan from Target that you wanted to screw around with, I can see where this might be tempting, but A/C units are expensive. I learned how to perform basic A/C maintenance and fairly simple repairs out of necessity (I owned businesses with creaky old A/C units and got tired of spending $1000 or more a month in the summer) but a homeowner with little to no A/C experience is wasting time and money - and increasing risk of harm - by trying to be a Johnny-Fix-Everything-Myself. Hell, these days I don't even change my own oil any more, since I can get a trained mechanic to do it quickly and cheaply. Oh, and I do not waste my time screwing around with A/C units, either: I figure my time is worth at least $30 an hour, and if I wasted 6-8 hours on a repair I may or may not be able to fix, that is waaaaay more than a service call.
5. Take a deep breath and get a reputable A/C technician to take care of this: it will be done in one-tenth the time, it will be done properly, and you will be cool in a matter of hours. Hell, with the 105 heat index today, the last thing I would want to be doing is messing around a shiny metal box in the hot sun.