Hello. I suspect this question seems rather ridiculous to most of you, but I'm a tad lost. How might I go about installing something with an extension .gz or .tar (like mozilla 1.7.5)? I know I need to extract files to somewhere, but I haven't the foggiest idea how to do it, or where to put the extracted files. Could somebody point me to a brief tutorial? Thanks.

For tar files, use 'tar -xvf filename.tar'. For tar.gz and tar.bz2 use 'tar -xzvf filename.tar.gz' and 'tar -xjvf filenmae.tar.bz2' respectively.
After that, cd into the newly created directory and look through the README or INSTALL file usually provided. It should be something like './configure' followed by 'make' and 'make install' for the installation.

if its a tar.gz file do tar xvzf file.tar.gz that will uncompress it into a directory of the same name.

You can also try mc. Open up a terminal and type: mc. That will open up a text based file manager. Usually in mc you can put the cursor over the tar.gz files and hit enter. That will open the tar.gz for viewing. You can then hit your insert key over the files and F5 to copy them where you want. Now if it's a file you downloaded in which you uncompress and after viewing the files you see the list and they include configure README and INSTALL. read all the docs first. or if you're willing to learn. type ./configure (let a bunch of shit run by) ./configure by itself will configure the app for installation to /usr/local. AFTER you configure it, if all goes well and you don't get errors... type make. then if all goes well with make and no errors come up about missing this and that ..... su to root. (do this by typint su) you will them be asked for the root password. the once you are root type 'make install'

Sounds to me like you might be better served looking in your distro's package manager and repository for whatever software you want rather than installing from .tar.