If you are in the Dropbox app on your iPad, go to the Public folder (you get it as a default with your Dropbox account - as far as I know).
Select a file within that public folder. Once it opens in the Dropbox viewing panel, in the upper right hand side, you'll see three symbols: links, a star and an arrow. If you click on the link icon, you'll get the choice to copy the link to the clipboard or to e-mail it. That's the public link to that file within the Public folder that you can share with anyone.
If you are on a PC, navigate to the Public folder within Dropbox. Once you are there, right click on a file and select "Copy Public Link." Then, you can just paste that anywhere you wish. I am sure the process is the same for a Mac, I just don't have one to tell you for sure...
Note that you cannot link directly to the Public folder, you can only link to a document within that folder.
Hope that helps.
Marilyn