How can I add new languages to Microsoft Office's spellcheck?

Check spelling and grammar in another language (Microsoft Office 2007)
or the
corresponding page for Microsoft Office 2010.

You have to install the Office Language Pack suitable for your language of choice. Which includes both languages changes to the interface (which you can enable or disable) and, the important to your case, language proofing tools.

You can alternatively purchase Multi-Language versions of Microsoft Office which already include several language packs.

Proofing Tools 2003 could be used on Microsoft Word 2003 and 2007. It cannot be installed on 2010.

A proofing tool for 2010 is supposedly "coming soon".