To better explain where I am, here is what I have tried so far: I've downloaded a lot of simple open source programs that have a lot of source files. But strangely, whenever I compile them myself and get them to run, it just runs on the command screen blindingly fast and then closes, as if I'm missing some important step. (How are you normally expected to compile open-source programs?)

Most open-source programs are made to be easy to compile on Unix platforms. If you're using OS X or Linux, great; if you're on Windows, download Cygwin and you'll have a Unix environment. Given all that, read the INSTALL file; it should give you step-by-step instructions for compiling and installing. Most commonly, you run ./configure, then make, then (as root) make install.

That said, platforms with package managers are really nice because you can download, build, and install many programs in a single step; Debian has APT, OS X has MacPorts and Fink, and Haskell (a programming language, not an operating system) has the Cabal.

In general, if running something causes a terminal to open and immediately close, try running it on a command line instead of double-clicking it. For Windows, open Command Prompt, drag the executable onto the terminal window, and hit enter.