Friendica has two different kinds of "address book".
The directory of the Friendica server you are registered on and a global directory to which your and other Friendica servers submit account information.
There are several global directories across the globe that regularly exchange information with each other.
The specific global directory that you see usually depends on where your server is located.
If you click through to the global directory, you will be presented with a list of everybody who choses to be listed across all instances of Friendica.
You will also see a "Show Community Forums" link, which will direct you to Groups, Forums and Fanpages.
You connect to people, groups and forums in the same way, except groups and forums will automatically accept your introduction request, whereas a human will approve you manually.
If your Friendica site is called "demo.friendica.com" and your username/nickname on that site is "bob", you would enter "bob@demo.friendica.com" in this form.
When you've submitted the connection page, it will take you back to your own site where you must then login (if necessary) and verify the connection request on *your* site.
Once you've done this, the two websites can communicate with each other to complete the process (after your new friend has approved the request).
You can also use your Identity Address or other people's Identity Addresses to become friends across the so-called Federation/Fedivese of open source social media.
Currently, Friendica supports connections with people on diaspora*, Red, Hubzilla, GNU Social, StatusNet, Mastodon, Pleroma, socialhome, and ganggo platforms.
If you know (for instance) "alice" on gnusocial.net (a GNU Social site) you could put alice@gnusocial.net into your Contact page and become friends across networks.
Likwise you can put in the URL to Alice's gnusocial.net page, if you wish.
Note: Some versions of GNU Social software may require the full URL to your profile and may not work with the identity address.
If you have supplied your mailbox connection information on your Settings page, you can enter the email address of anybody that has sent you a message recently and have their email messages show up in your social stream.
Once you have become friends, if you find the person constantly sends you spam or worthless information, you can "Ignore" them - without breaking off the friendship or even alerting them to the fact that you aren't interested in anything they are saying.