How do I spell and grammar check in another language?

If it is just a matter of spell checking in one document, you can change the dictionary in the Inspector > T > Other > Language. The language will be set for all currently highlighted text. Warning: when you change style, the language may also change.

If you want all new documents to use spell checking of another language, you have to go through the following steps, for each template you intend to use.

1. Open a new document with the template you want to use.
2. Open the Styles Drawer (View > Show Styles Drawer).
3. Select the first style in the list. (This is often "Free Form".)
4. Change the language in the inspector as described above.
5. Click on the red triangle to the right of the style name in the Style Drawer, and in the menu that pops up, choose "Redefine Style from Selection".
6. Repeat steps 3-5 for every Paragraph Style in the Style Drawer.
7. Go to File > Save as Template, and choose a good name of the template.
8. If you have only one template you always want to use, you can choose it in Pages > Preferences > General > For New Documents, where you select "Use template:..." and then click on Choose... and choose the template.

And now for some additional hints:

Note that you can have several styles in the same document for different languages. You can for example have one style called "French body" and another called "Italian body". You can even associate shortcuts to the styles, in the Styles drawer, so you quickly can change between one language and another.

Another way to change language spelling is to quit Pages, go to System Preferences > International > Language, and drag your favourite language to the top. Then restart Pages. The inconvenience here is that all menus change as well, even in other applications as they start.

If you want spell check in a language that is not supported by Apple, you can try the free CocoAspell by Anton Leuski. CocoAspell claims support for languages like Afrikaans, Amharic, Arabic, Azerbaijani, Belarusian, Bulgarian, Bengali, Breton, Catalan, Czech, Kashubian, Welsh, Greek, Esperanto, Estonian, Persian, Finnish, Faroese, Frisian, Irish, Scottish Gaelic, Galician, Gujarati, Manx Gaelic, Hebrew, Hindi, Hiligaynon, Croatian, Upper Sorbian, Hungarian, Armenian, Interlingua, Indonesian, Icelandic, Kurdi, Latin, Lithuanian, Latvian, Low Saxon, Malagasy, Maori, Macedonian, Malayalam, Mongolian, Marathi, Malay, Maltese, Norwegian Bokmål, Norwegian Nynorsk, Chichewa, Oriya, Punjabi, Polish, Quechua, Romanian, Kinyarwanda, Sardinian, Slovak, Slovenian, Serbian, Swahili, Tamil, Telugu, Tetum, Turkmen, Tagalog, Setswana, Turkish, Ukrainian, Uzbek, Vietnamese, Walloon, Yiddish, Zulu. Pages does not support all those languages, but CocoAspell works with other applications as well.