A photo is just about the only thing you can directly upload from the DropBox app. Just tap on the camera icon at the bottom right and select a photo to upload.
The iPad does not have a shared file system. Each app contains it's own file space, pretty much owning anything in that space. This makes working with files a bit different from how you are used to doing it on a computer. Instead of finding a file and opening it in an app, you open your app and find the file.
Some apps directly support DropBox. You can set up your DropBox account in the app and go directly there to upload and download files from that app. GoodReader is probably one of the more useful of these apps. It handles a large number of file types for viewing. Many apps can send files to GoodReader via the Open In.. feature, and if the app supports it GoodReader can send files to that app using the Open In... .
As an example of how Open In works, find one of those sample files in your DropBox, one of the Get Started pdf files, not a picture. Select it and let it download. Now tap on the share icon at the top right of your screen. It looks like a box with an arrow coming out of it. You'll see a list of compatible apps that you can open the file in. If you have iBooks or GoodReader they will appear. Note, that app has to not only be able to read the file, but has to register itself with iOS as compatible with that file type. Not all apps do this. So you might not see any in the list.
All in all, it's a bit of a dance finding the right apps for what you want to do. That's a big part of what the forum is about. Use the search to try and find the things you want, and if that doesn't work go ahead and start your own thread and ask. But you already know how to do that.
If you don't have it, I recommend getting the iPad Users Guide. You can download it for your computer with the following link. I also recommend getting the iBook app from the App Store. Once you have it go to the iBook Store in the app and get the iPad User's Guide there. Both are free.
iPad Users Guide
http://manuals.info.apple.com/en_US/iPad_User_Guide.pdf