Friendship in Friendika can take on a great many different meanings. But let's keep it simple, you want to be friends with somebody. How do you do it?
The first thing you can do is look at the Directory for somebody you would like to connect with. Visit their profile. Just beneath their profile picture will be the word 'Connect' (we're assuming this is an English language profile).
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 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 email@example.com into your Contact page and become friends across networks. (Or you can put in the URL to 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 Friendika. 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 Friendika.
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 Friendika Identity Address into their identi.ca subscription dialog box.
Some networks allow people to send you messages without being friends and without your approval. Friendika does not allow this by default, as it would open a gateway for spam. So when you've approved a friend request from one of these networks, look at your contact page for that person (this will be displayed as soon as you approve the relationship). They might be marked as an "Ignored" contact.
This means they can see some of your posts (your public posts), but they aren't permitted to send you anything. You can "Un-ignore" them if you desire to allow them to contact you directly and to have their status updates appear in your Network feed.
When you receive a friendship notification from another Friendika 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 in any way. They will know or be able to discover that they have been blocked but there's nothing they can do about it.
You can also delete a friend no matter what the friendship status - which complete removes everything relating to that person from your website.