A simple way to update Firefox (and other Mozilla software) is to add this link as a Software Repository (if you have a good connection to the Internet):
Using either Yast -> Software -> Software Repositories, or right-clicking the openSUSE Updater applett and selecting Add/Remove Update Sources, you would add a repository of:
Repository Name (A description that is meaningful to you)
Directory on Server repositories/mozilla/openSUSE_10.3
Leave everything else at its default, click OK, then (optionally) Refresh Now, then Finish. Now, you can update Firefox the same way you update openSUSE. The updates come pretty quickly after Mozilla releases an update, but (be aware) not always.
You can get the Mozilla .tar updates to work, but it is more complex to do so and fairly undocumented (as far as I can tell). Whether or not to try it depends on your patience.
Welcome to open source software and Linus. Have fun.