It seems iCloud Drive as of today only works under www.icloud.com (you have a new app inside your web account, just go there and you'll find it). You can upload and download any file and do things exactly like Dropbox. On your iOS device, you will find your documents automatically inside the app that is working also through iCloud. If you open Pages, you will find any document automatically in your cloud. If you save a new one, it will appear inside iCloud Drive in the web app.
There is no iCloud Drive App on your iOS8 device as of now. Maybe Apple is releasing it later. I don't see why they should, since it works automatically anyway, but since there were screenshots of this on Iphone and Ipad, I guess they will. I would prefer to have an app for this, like DropBox, but even if there was no app, no big deal: it already works perfectly inside other apps. (for now just Pages, Keynote, Numbers and a few others, but I guess updates to other apps will adjust this problem).