In case this helps any fresh beginners:
I asked my original question because I thought running the flex samples was something that could be done easily from notepad, but it is not that simple. You need a program that can build/compile flash files (once created these are .swf files). It seems that the most common is Adobe Flash Builder. You could try FlashDevelop, a free program, but personally I am still having some trouble getting maps to show with this program. The program you choose will be where you copy the sample code and run the sample. It should run in a window produced by the program as opposed to popping up in an internet browser.
You need to have two resources set up in your program in order to run the flex samples found in the arcgis API for flex. Instructions for this may vary with the program you use. Both are free online downloads.
1. the flex SDK (software development kit). this makes it possible to...well, do flex things. it is a folder full of folders of necessary things!
2. the arcgis API for flex must be set up. this makes it possible to do GEOGRAPHIC flex things. the file extension for the "library" you need to add to your project or program is .swc
A flex project contains multiple files. Make sure you copy the code in to the correct file of your project.
Maybe it was just me, but I needed some more dummy-proof explanation of how to get set up to use flex and the arcgis API, so I hope it helps someone.