How to set your profile to private / public

To set your profile to private/public, You can set your desired settings in the privacy section of facebook:

Move your mouse over the "Account" in the top right corner and click "privacy" (ie. https://www.facebook.com/privacy/ ).

Then click on "Profile" (ie. https://www.facebook.com/privacy/?view=profile )

If you set the "Profile" option to "Only friends" then only friends will be able to see your profile. This includes pictures and info. Changing it to "everyone in my network" will allow everyone that's in your network(s) to be able to see your profile.
Once you save this option anyone that isn't your friend that searches for you will see your name in black (ie. non-clickable) and they will need to add you as a friend (and you accept the request) for them to be able to see your profile & pictures.

There is something else people may want to know if your profile is set to everyone unclick a box that say "Create a public search listing for me and submit it for search engine indexing" this means your profile will appear on a google search yahoo etc.
I also wanted to correct you funnytim its not under "profile" its under "search" its easier, under profile is for limiting access to your profile if it is set as "everyone".

The Public search listing you mentioned above, as well as the search visibility is under search yes, however under "Profile" is where one can set your profile status to "everyone (in your networks), only friends", etc.

Thanks for the additional information on the Public Listing feature, I did not think of mentioning it