what basic word processing application for osx would you recommend?

I'd use either Word or LibreOffice Writer (formerly OpenOffice, but that project was forked and the 'original' is basically defunct) to write, and DropBox to store it. Oh, and other backups too, since DropBox doesn't prevent other kinds of Bad Things like accidental deletions.

I've processed words and published manuals on Macs since 1985. I've hated Word since 1.05 and that's an unnatural prejudice I'm sticking to. I've relied on Pages since 2008. I've never encountered wacky bugs—but I'm not using 10.9 yet (no reason to). Using Pages, I've made signs, posters, pamphlets, copy-for-publishers, and blog posts; I've printed locallly, handed PDFs to copy shops for big color output, and exported .DOC (Word format) files. Pages handles tables which Word bombs on. At least v4.3 is a remarkably intuitive WP; it's easy to turn off all the formats and write, and it's painless to assign keyboard commands and slap in formats at will. I have not seen the current version. Unless you're using anhttp://www.adobe.com/products/framemaker.html, more important than the WP is your workflow: don't keep your document in one file. Break it down into meaningfully large but not-more-than-40 pages. When you're finished with a chunk, then you can merge it with other finished bits. Save often; save a new version of the working file every day. The magic of undo means your files get tangled: saving new is the best prevention in the world. I've also used Nisus Writer Express http://nisus.com/Express/ and its big brother Nisus Writer Pro. They include a lot of features for data processing (sophisticated search and replace, columnar selection, discontinuous selection (Pages does that too)) but the WP features feel a little tacked on. I never could figure out their Styles system, and formatting with styles, not locally, is essential if you're submitting a book manuscript.

If she bought the Mac recently, I believe she may have Pages included, which is Apple's answer to MS Word.

I was going to suggest OpenOffice too. I wrote my dissertation on it with no problems.

I have a Mac and it comes with iWork but I'm not a huge fan. If she's used to Word I'd just get Office for Mac. Especially if she is ever going to need a spreadsheet, because Numbers is awful.

I recently switched to Mac from Windows and decided not to shell out for MS Office. The LibreOffice Calc application is actually quite nice and comparable to Excel unless you're doing complicated macro programming. I've been less happy with LibreOffice Writer, their Word equivalent; the page breaks are annoying as hell to delete/move around and the menu is pretty different. So I've switched to Google Docs for word processing, which suits basic needs; however, I do all my complicated word processing, such as my thesis, in LaTeX which is a decidedly technical option. For word processing, I'd say try out LibreOffice and Google Drive, see which she likes better. Scrivener is reportedly super-awesome for novel writers, which may or may not suit her use case.

This is a Mac user. Why all of the Word recommendations? My comments: Scrivener is great, but it has a modest cost - $45. It is NOT for the "not very techie" user, though. Writing in it is simple; getting it into print or PDF-ready format can be a bit of a challenge. The strongest point in its favor is its tree-organizer format, which is a godsend for a long writing project. Pages is now, I believe, now $20 in the App Store, or free with many Macs. I am not sure how it would work if she wants to generate a table of contents, etc. but for most purposes it is an excellent choice. Apple, perplexingly, dumbed it down with the switch to the App Store version, but gradually has been restoring its higher-end features.

It's no longer being developed, but I used to love http://www.bean-osx.com/Bean.html. I now use Scrivener but it is a different animal.

No personal experience, but http://nisus.com/ make two word processors, the simpler of which is $45. It would be worth checking out reviews & getting other opinions, but they seem to have their advocates. I use Pages (older version) and find it good, but have no idea how it would go with larger & more complex documents.