The first thing you can do is look at the Directory. The directory is split up into two parts. If you click the directory button, you will be presented with a list of all members (who chose to be listed) on your server. You'll also see a link to the Global Directory. If you click through to the global directory, you will be presented with a list of everybody who chose 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.
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).
If you already know somebody's Identity Address, you can enter it in the "connect" box on your "Contacts" page. This will take you through a similar process.
You can also use your Identity Address or other people's Identity Addresses to become friends across networks. The list of possible networks is growing all the time. If you know (for instance) "bob" on identi.ca (a Status.Net site) you could put bob@identi.ca into your Contact page and become friends across networks. (Or you can put in the URLto Bob's identi.ca page if you wish). You can also be "partial" friends with somebody on Google Buzz by putting in their gmail address. Google Buzz does not yet support all the protocols we need for direct messaging, but you should be able to follow status updates from within Friendica. You can do the same for Twitter accounts and Diaspora accounts. In fact you can "follow" most anybody or any website that produces a syndication feed (RSS/Atom,etc.). If we can find an information stream and a name to attach to the contact, we'll try to connect with them.
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. You can also reply to them from within Friendica.
People can also become friends with you from other networks. If a friend of yours has an identi.ca account, they can become friends with you by putting your Friendica Identity Address into their identi.ca subscription dialog box. A similar mechanism is available for Diaspora members, by putting your iendtity address into their search bar.
Some networks allow people to send you messages without being friends and without your approval. Friendica does not allow this by default, as it would open a gateway for spam.
When you receive a friendship notification from another Friendica member, you will have the option of allowing them as a "fan" or as a "friend". If they are a fan, they can see what you have to say, including private communications that you send to them, but not vice versa. As a friend, you can both communicate with each other.
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. In many ways they are like a "fan" - but they don't know this. They think they are a friend.
You can also "block" a person. This completely blocks communications with that person. They may still be able to see your public posts, as can anybody in the world, but they cannot communicate with you directly.