There is no direct way of doing it.
If you are willing to pay a small monthly fee, DropDAV will let you connect to your DropBox account using the WebDAV import/export options in Numbers.
sendtodropbox.com will give you an email address that will deposit email attachments in a folder on DropBox. You have to move them manually after they arrive, which can take a while depending on the sendtodropbox server's load.
You can email them to yourself, then use the Open In... feature in Mail to copy them to the DropBox app. It will take you to the upload screen/options automatically.
In some cases you will be creating a new file, not replacing/syncing with the old one. In others you may have the option to replace the old file. There is no way to automatically sync the file at this time.
Or you can wait for iOS 5 and iCloud to see how it works there.
Thats all I've got.