you're using the "public" folder correct? it can't be shared...and i wouldn't share any folders with "everyone".
when you drop the file in the public folder...it has to sync the files between your system and dropbox...so the dropbox client has to be running and until the file has a green circle with a check mark in it, the file won't be accessible to anyone...takes a while to synchronize sometimes.
now, if you have the dropbox client running on your system...and you navigate to the public folder...find the file you placed in there and right click it...you should see a line that is labeled "dropbox"...hover your mouse cursor over that and you will see a dropdown menu to the right...you should see an option labeled "copy public link"...click on that, it will automatically create a url link for you to paste into wherever and turn it into an active link.