Oh heck. I thought you had a word processor on the iPad. I'm mac-averse, so I have a Nexus. That said....
Here's the Dropbox on iPad app:
https://www.dropbox.com/ipad
Here's something that might work for editing:
https://www.rollapp.com/openoffice There's a comment on a forum that this operates "in the cloud", so you need to be connected to use it, but I'm not sure if that's true, or how true it is, or how often you'll be offline with your iPad.
It's Google Drive, not Google Docs. My mistake. Box is also mentioned as an similar program.
Basically, Dropbox will create a Dropbox folder on your PC linked to your Dropbox account. Any files placed in this folder will update the online version. Open the Dropbox file, work as usual, and save. When you switch to another device, open the dropbox file again, work as usual, and save. I'm pretty sure you can open and edit files wholly in the cloud as well, so you could open a file from someone else's computer without installing dropbox (just go to the site and log in to see your files) and work on it.