installing binary packages with a gui is a breeze. Try synaptic package manager (should be included with mepis).
compiling from source is another level of pancakes. But it can be simplified into 3 "easy" steps on the command line (from the source's directory):
3) make install
1) configure will check for the compilers, libraries, and other dependencies that the source requires to be compiled. There are usually options that you can turn on while doing a configure ie ./configure --with-mysql (turns on mysql). You can find out what options you can enable with a ./configure --help. If it fails, that usually means you are missing a dependency: look at the error message, search synaptic for the *-dev package, and install it. If you can't find the package, google probably will help you determine where/what it is.
2)make - this compiles the source. Sometimes it will fail with errors because of a dependency that configure failed to detect (usually bad on the developers for that). Once again, look at the error message and search for the missing library in synaptic/google.
3)make install - this copies the newly compiled source to your system where it can be used by you. This is the only step that will require root privileges.
That should at least get you started. Here is a good podcast on various Linux topics for newbies: http://www.linuxreality.com/podcast/...g-from-source/