You cannot access anyone’s Public Dropbox folder unless they’ve given you the link to it.
There’s a common misconception that Dropbox folders are listed in a directory of drop boxes somewhere, and people can put files in and take files out anytime they want to at some mysterious location, if only someone would tell them where it is.
Dropbox is not a public post office. There is no manual of zip codes. You can’t ‘find’ people on Dropbox. Neither can you ‘view’ another person’s Dropbox files unless they want you to. You can only send files to another person’s Dropbox by having a shared folder with them. (Read about how to share a Dropbox folder.)
Your Public Dropbox folder is simply a default folder created during the installation of Dropbox on your computer. (As of October 4, 2012 Public folders are no longer a part of the Dropbox installation.) You can use it or not use it. Some people use it as a place to put all the files they want to share publicly. It’s not necessary, just a convenience.
(You can do the same thing by creating a folder called XYZ. The point is in the link itself. If you publicly post a link to a folder in your Dropbox, it’s public.)
If you share only links to individual files within the Public folder, or any folder, that’s all someone else can see. You can share the link to the whole folder in which case all the files in it, present and future, can be seen by anyone who has the link.
If you don’t have a Public folder, just create a new folder name Public. It will work exactly the same.
To share a link to an individual file within the Public folder:
Right-click on the file, and choose Dropbox/Copy public link
If you have installed Dropbox since October 4, 2012, it might say Share link instead. It doesn’t really matter. Either way you have a link to share.
The link is now on your clipboard so you can paste it into a web page or email. The person who receives this link will only be able to see the specific file you sent them a link for, not the other contents of your Public folder.
To share a link to your entire Public folder, right click on the Public folder and choose Dropbox/Get link.
This will open your browser to the contents of your Public folder and you can copy the link from the address bar and paste it wherever you want.
Think twice about whether you want the link to your entire Public folder, or any folder, made public because once you give it away you can’t take it back.
The search engines do not index these links unless they’re posted on web pages. To stop sharing a file, simple remove it from your Public folder.