First, you should have Dropbox installed on your main computer as well as on the iPad... If you just have it on the iPad It's not that useful.
I use Dropbox as an easy method to 'put' PDF and Word files on my iPad. I copy them to the Dropbox folder on the main computer.. Then, when I open Dropbox on my iPad, I can read them using iPad apps. There is an option in the iPad Dropbox to "Open With".. I open PDF files with the Adobe reader app and I open Word files with the 'GoodReader' app. Once you've opened a document, that document gets 'uploaded' to the iPad and is always there to read when you're offline..
As far as sharing... When you install Dropbox on your main computer, you should see a PDF document explaining how to use it.. There are instructions there on how to set up a public directory where you can share files with friends...