I dunno about using .tgz or whatever in Fedora, but do you know what an RPM is? RPMs are comparable to windows type installers (one click), only problem is, often times you end up having to get tons of other packages, or dependencies just to get the original program to work.
To compile from source, get the "source code" version of a file (most likely .tgz or .bz2). Unzip, untar Ark or whatever (extract) the file to a folder. Open a terminal that is in that folder. If in KDE, right click>actions>open terminal here. If in Gnome, I dunno, but you can find out! Once you are in the directory of the extracted archive, and in the terminal, there should be some sort of comfiguration script. It will most likely be called "configure" . To run it, in the Konsole type "./configure" or "sh configure" . there may be other similar install scripts varying due to the program. try to find a readme or install file on the web page or with the archive. Once configure is done type "make" . this should take awhile. It is compiling or making custom for your system, the program, After make is finished type "make install" . After that type the name of the program or something in the command prompt, it should start the program.
Some programs run directly from a directory. If you see the name of the program in something that looks like the program, try typing it preceded with "./", "sh", or just type the name. Make sure you have a ?C compiler such as GCC. If you'd post back about the specific program and stuff I'm willing to help.
Sorry for the long-windedness, best of wishes, and good luck!
Need more help?