An alternative to using the Profile manager (the -P
switch described in @hasen's answer) is to specify the path to profile directly in the command line.
firefox -no-remote -profile absolute-path-to-the-profile-dir
will create the directory specified (if it doesn't exist) and use it as the profile.
Example on Windows:
C:\Progra~1\Firefox\firefox.exe -no-remote -profile C:\FxProfiles\myprofile
On OS X it is slightly more complicated:
/Applications/Firefox.app/Contents/MacOS/firefox-bin -foreground \
-no-remote -profile /Users/me/fx-profiles/myprofile
-foreground
switches from the terminal window to Firefox. Note that on 10.5 you have to use an even more complicated comand to work around the dyld
error.
See also Starting Firefox with a specified profile from the dock (Mac OS X).