You always have a profile known as your "default" or "public" profile. This profile is always available to the general public and cannot be hidden (there may be rare exceptions on privately run or disconnected sites). You may, and probably should restrict the information you make available on your public profile.
In addition, if you'd like to meet people that share some general interests with you, please take a moment and add some "Public Keywords" to your profile. Such as "music, linux, photography" or whatever. You can add as many keywords as you like.
Your default or public profile is also shown to contacts on other networks, since they do not have the ability to view your private profiles. Only members of the Friendica network can see alternate/private profiles.
To create an alternate profile, select "Profiles" from the menu of your Friendica site. You may edit an existing profile, change the profile photo, or create a new profile. You may also create a "clone" of an existing profile if you only wish to change a few items but don't wish to enter all the information again.
To assign a profile to specific persons, select the person from your "Contacts" page and click the pencil "Edit" icon. You will find a dropdown box listing the various profiles available. If this box is not selectable, the person is not in a supported network and cannot be assigned a specific profile.
Once a profile has been selected, when the person views your profile from one of the "magic profile links" on their site, they will see the private profile you have assigned. If they are not logged into their site or view your profile from elsewhere, they will see your public profile.
A magic profile link is indicated by a special cursor when hovering over a contact's name or photo. Currently this cursor is a hand next to a small padlock. These magic cursors indicate that by following the link, you are able to access special areas of the other person's pages which are only available to friends and may not be available to the general public.
You may also discover that (assuming you have the proper permissions) you may be able to post directly on the other person's profile (often called a "wall-to-wall" post). You may also be able to comment directly on posts from while visiting the other person's profile page.
There are two settings which allow you to publish your profile to a directory and ensure that it can be found by others. You can change these through settings on the "Settings" page. One setting allows you to publish your profile in the site directory of this Friendica server. Another option (this may have been disabled by the site creator) allows you to publish your profile in the "Global Directory". This is a mega directory which contains people from many other Friendica installations world-wide.
If you do not wish to be visible to any of these sites, you may leave your profile unpublished.
Although you may have multiple profiles, you only have one profile photo. This is intentional. In early tests we experimented with different photos for each profile and found it was very confusing for people. They might see a different picture depending on what website they visited or what conversation they were in, and often alerted them to the fact that other people might be able to see different profiles of you than they could see.
(But you can use the rich-text information boxes within a profile such as "Tell us about yourself" and link other photos onto the page.)
On the site Directory page, you may search for people with published profiles who are on this site. The search is typically for your nickname or part of your full name. However this search will also match against other profile fields - such as gender, location, "about", work, and education. You may also include "Keywords" in your default profile - which may be used to search for common interests with other members. You have two sets of keywords available - public and private. Private keywords are *not* visible to anybody. You could use these keywords to locate people who share membership in secret societies, or that share a love of fishing (for example) - without making this information visible on your public profile. Public keywords are used in the friend suggestion tool and although they aren't readily visible, they may be seen by viewing the HTML of your profile page.
Directory searches are also able to use "boolean" logic so that you can search for "+lesbian +Florida" and find those who's sexual preference (or keywords) contain the world "lesbian" and that live in Florida. See the section on "Topical Tags" on the [Tags-and-Mentions](help/Tags-and-Mentions) page for more information on performing boolean searches.
On your Contacts page is a link to "Find People with Shared Interests" (unless your site administrator has disabled the global directory). This will combine both your public and private keywords, and find people in the global directory who have matching and/or similar keywords. (Your private keywords are not identified or stored on the global directory). The more keywords you provide, the more relevant the search results that are returned. These are sorted by relevance. You may discover that you are the first person on the list - because you are very likely the most relevant match for your keywords in the directory.