The iWorks apps do not work directly with DropBox. It is possible to use the Open In feature in the DropBox app to open a file in an iWorks app, but it is not possible to save a file directly from iWorks to DropBox, at least not without a third service. There are two that I know of.
DropDAV works very well by providing a WebDAV interface for DropBox; however it requires a monthly fee.
mailtodropbox.com will let you send iWorks files to DropBox via a supplied email address. It is slow, and the attachment can only be copied to a special Attachment folder, but it is free.
Box.net is a decent alternative for iWorks, as it has free WebDAV support. However unlike DropBox you can not sync with a local folder on your computer; unless you pay for a business account. That means you must manage your files from a web browser on the computer. Or you can mount the WebDAV service to your computer, and it will behave like a (very slow) hard drive.
I'm not familiear with how well QuickOffice works with DropBox, though I understand it does. I'll leave that to someone else to supply the details.