well, you should try to use root as little as possible. for instance, i would recommend never ever ever browsing the internet or downloading anything as root. you're just asking for trouble. here's how i installed firefox: i grabbed the mozilla-firefox-1.0.4.tgz from slackware-current and downloaded it to /home/mcd/downloads, then opened an xterm, cd'd into that directory, and typed installpkg mozilla-firefox-1.0.4.tgz. i only use it as my user, never as root. all my downloads go into /home/mcd/downloads, and once they're there i can move them wherever i like.
i'd also like to say a few words about /bin, /usr/bin and links. basically making a ln -s is like making a shortcut. now, when you open an xterm or equivalent, it remembers what's called your PATH. this typically includes /usr/bin, /usr/sbin, /usr/local/bin and a few other locations. that means that you don't have to type out the full pathname for binaries in those directories. imagine that there exists /usr/bin/firefox ok? normally you need to run it by either typing /usr/bin/firefox, or by cd'ing into that directory and typing ./firefox (./ = current directory). but since /usr/bin is in your PATH you don't have to type out the full name - just type firefox from wherever you are and it will run. so if there's something (like firefox) that you use a lot, it's worth making a link in one of the directories in your PATH to save yourself typing out the full location of the firefox executable every time. i hope that makes sense.
however, there's another way to save yourself typing, which i sort of prefer. every user has a file in their home directory called .bashrc (mine is /home/mcd/.bashrc) where you can create (among other things) aliases. i have one like this:
alias firefox='/usr/local/bin/firefox'
alias thunderbird='/home/mcd/src/thunderbird/thunderbird'
and this means every time i type firefox it automatically substitutes the full pathname. there are a lot of other neat things you can do in your .bashrc, if you're curious you can take a look here:
http://www.tldp.org/LDP/abs/html/sample-bashrc.html
anyway, i hope all that's not too confusing.