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
See also Starting Firefox with a specified profile from the dock (Mac OS X).