When I implemented compat32pkg I wrote an howto
about using firefox 32 and 64-bit at the same time.
If you don't want to use compat32pkg to install 32-bit firefox, you will have to proceed as below (slackware 13.37) :
$ wget ftp://slackware.mirrors.tds.net/pub/slackware/slackware-13.37/patches/packages/mozilla-firefox-17.0.11esr-i486-1_slack13.37.txz
$ convertpkg-compat32 -i mozilla-firefox-17.0.11esr-i486-1_slack13.37.txz
$ installpkg /tmp/mozilla-firefox-compat32-17.0.11esr-i486-1_slack13.37.1compat32.txz
Slackware 13.37 comes with an old JRE which must not be used. So, It's better to use the slackbuild in /extra from Slackware 14.1 to create a package, then convert it to compat32 and install this last one :
$ ./java.SlackBuild /path/to/jre-7u55-linux-i586.tar.gz
$ convertpkg-compat32 -i /tmp/jre-7u55-i586-1.txz
$ installpkg /tmp/jre-compat32-7u55-x86_64-1compat32.txz
At this point you should have 32-bit firefox and jre (with its plugin) installed.
To start 32-bit firefox, you will have to run /usr/bin/32/firefox. Note that if you want to use 32 and 64 bit firefox at the same time, you could have to create profiles as pointed out in the compat32pkg's howto
Hope this helps.