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 Groups" link, which will direct you to Groups.
You connect to people and groups the same way, public groups will automatically accept your introduction, whereas private groups and some individual users will need to manually approve it.
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 log in (if necessary) and verify the connection request on *your* site.
You can also use your Identity Address or other people's Identity Addresses to become friends across the so-called Federation/Fediverse 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.
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.