People move about, which means that every time you refresh the Public Worlds page different worlds may appear at the top. I suggest you refresh the Public Worlds page and then immediately go to the world at the top left of the search results (that should be the public world that currently has the most people inside it).
Looking at my admin control panel I see you're currently in a public world with 2 other people inside it, so I guess you already figured this out
Private worlds are, as their name implies, private, so you can't find them unless someone gives you a link to their world page. You can find them on the world map in the viewer but you'll be blocked if you try to teleport into them. Some private worlds' world pages are advertised on people's blogs but if you aren't a member of that community you aren't likely to encounter them.
If you do get to a private world's world page (one which you aren't already allowed to enter) you can use the option on that page to send the world manager a message to request that he or she grant you access to that world.
