Note: Some of these views are my own and may not be exactly the same as others in the daemon community.
What is daemonism?
Daemonism is the philososphy that it is helpful to actively communicate with "the second voice in your head", i.e., a daemon. There is no belief, or faith, in the paranormal, occult or in a higher being needed. A daemon is, by definition, part of yourself and your mind - no-one can say, "You don't have a daemon" because that is like saying, "You don't imagine things". A daemon is part of YOUR MIND, and no-one else can say what is in your mind.
What is a daemon?
A daemon is a mental construct that helps you through life, is your constant companion, and the other half of you. It is the voice that acts as your conscience and the one that replies when you ask yourself a question. Daemons are an internal (imaginary, though that detracts nothing from their importance) construct, and part of you, and not an external spirit or higher power. Everyone has a daemon, as everyone has an imagination. The name "daemon" is taken from Philip Pullman's His Dark Materials, but in our real world we don't treat daemons as corporeal beings, nor do we pretend that they are - we just think they exist. There isn't a physical crow sitting in front of me, but I can imagine one.
Going further, and actively reaching out to that half-unconscious side of you that is your daemon, and trying to talk and visualise them, is daemonism.
A daemon's "physical" form, or at least in your mind, is an animal which best fits and personifies your personality. For example, someone who has a intimidating, powerful personality and likes to be alone may well have some kind of large cat daemon.
How can I find my daemon?
Ask a question in your mind - the replying voice is your daemon. The second voice that answers your thoughts sometimes is your daemon. You just have to get to know them more, so that it becomes easier to tell which voice is yours and which is your daemon's. Listen to the daemon's "voice" - is it different from yours? Is it clearly a "male" or a "female" voice? The majority of people have a daemon of the opposite gender - this is probably because it fits the other half of you, and is what you need to help you.
Visualising is a great aid. Think of any animal - one you've seen often and that is easy to visualise how it moves would be good. Visualise it in front of you, or beside you, or wherever you think a daemon should be (on your shoulder?), and talk in this way. Visualising is the only way you'll know when you're settled.
What's settling?
Settling is when your daemon ceases to change shape and settles as one form. My daemon is settled as a crow of some sort, meaning that I as a person am a scavanger, remarkably intelligent and also rather annoying. There is NO NEED to think "OMG what's my settled form?!" because it WILL come in time. Most people settle their personality and character around 15-20, so don't worry. You don't need to stress about it, you will both know when you're settled.
For animal analysis's, visit The Daemon Forum.
What's my daemon's name?
Daemons, like you, don't come with an automatic name. You'll have to discuss with yours what a good name will be. My daemon is Zephiron-Shujiro Karaioh (he wanted a long fancy name ... ), for example, but others have simpler (or even fancier) names.
Why do I want a daemon?
Who wouldn't want a friend who is always with you, is your best adviser, constantly guides you in life, loves you unconditionally and is your character personified? When your daemon settles, that animal will tell you an awful lot about the kind of person you are, which is no doubt very useful.
Now what?
Want to know more about the daemon community? The Daemon Forum is the site for meeting other daemians, and is also one of the friendliest and nicest (and also the most literate) forums out there. Also check out the other sites in the Daemon Webring.