It's easier than you think.
It is important to remember that your dæmon can only exist in your own mind. You will not be able to physically see, touch, or hear your dæmon the way you can see, hear and touch the people around you.
At first, your dæmon's voice will just sound like your normal mental voice, although eventually he or she will start to develop a unique tone. This is reality, not fantasy.
Your dæmon is as real as you are. The human mind is a complex thing. You are simply going to find an unconscious part of your personality, and embrace it. By giving it a gender, a body, and a name, we are better able to interact with that hidden part of our selves.
Not at all. Jung believed that it was extremely healthy and necessary for us to understand ourselves and reach our full potential. Similar techniques are used by many religious and spiritual people, but even hard headed scientists have recognized the power of the human imagination to emotionally heal people. For example, the imaginary friend is an extremely common childhood phenomenon. It is also considered to be a very healthy phenomenon. Children with imaginary friends are usually more advanced in their verbal and social skills. Imaginary friends often help children adjust to new social situations, increasing their confidence. The friend's personality is often complimentary to the child's, being outgoing where the child is shy, for example. This is another example of the hidden self. These imaginary friends that children have are simply the children's way of getting in touch with their "dæmon." When you find your dæmon, you may find that his or her personality compliments your own. That is because your dæmon is the part of you that has been suppressed.
Probably, or at least a version of your dæmon. Many dæmians report having, as children, pictured an imaginary animal running outside their car, or following them around at school. Like Pullman's dæmons, the animal may have changed shape according to the person's mood that day. As the dæmian grew older, though, they may have forgotten their friend entirely, or started picturing him or her less often.
Even if your imaginary friend was a human, this may still have been an attempt on your part to get in touch with your dæmon. Dæmons generally have animal forms, for several reasons.
1) It is easier and probably more comfortable to imagine an animal as your constant companion and guiding spirit than another human being. Another human would seem like a separate individual, rather than a manifestation of your subconscious or soul.
2) Animals take on a symbolic quality - often the form of our dæmon tells us a lot about ourselves. The animal as a symbol of personality is a universal concept: from the animals of the Chinese Zodiac, to Native American totems, to J.K. Rowling's patronus.
If you never had an imaginary friend, don't worry. You still have a dæmon. But you might find it harder to get in touch with that part of yourself, because it involves powers of imagination which you may not have exercised before.
Start small. Start listening for that little voice in your head. It's the part of you that comments on your actions, like saying "Well, that wasn't smart" when you do something stupid, or that says "Go to bed!" when you are up at two in the morning. This is the part of you that watches yourself. Start answering back. If you find yourself having a conversation or even an argument in your head - congratulations, you are on your way to finding your dæmon.
Other people start with trying to visualize their dæmon first. Since your dæmon lives inside you (at least in this world), you need to imagine or "project" him or her so that you can picture him/her. Some people always project their dæmon when they talk to him or her, and some people don't need to. Start by imagining an animal of some kind - it could be a bird or a dog, a raccoon, or any other animal you feel comfortable imagining. You don't have to try and talk to it yet. It doesn't have to be the animal that best represents you as a person. This is just a start. Try imagining the animal investigating your room, or looking at whatever you are working on. If there are people in the room, try imagining it reacting to what they say and do.
Next try putting those two things together. The next time you tell yourself to go to bed, or you start trying to make a mental list, or you think sarcastic things about somebody you work with, imagine the animal saying those things. This is the process of separating the voices in your head.
You may be able to see, now, why this is healthy. Most people have a clamor of mental voices, all their own. They think circular thoughts, like "I have to go to bed. But I have to finish this assignment. But I'm exhausted, I need sleep. But I have to present this tomorrow." Or they might be in a store, trying to decide on a pair of shoes. "These are too expensive. But they're good quality, they'll last for a long time. But I haven't budgeted this much money. But I need a good quality pair if I'm going to be standing up at work all day."
By separating your own voice from your inner voice, you can start focusing on what you want, versus what your subconscious is thinking. You will be better able to make rational decisions, and you will feel far less conflicted. You will know that your dæmon wants you to get some rest, but that you really want to finish the assignment. Dæmons often function as a sort of Jiminy Cricket, voicing concern for your welfare, the morality of your decisions and so on. However, everybody's dæmon is different. The person who has always been very moral, always followed every rule, may find that his or her dæmon is a voice of mischief which they have suppressed. Allowing your suppressed side to have a voice can be very liberating. You may end up finding yourself smirking because of a rude but silent comment your dæmon just made.
For some people, the dæmon comes very easily. Often these are people who have had imaginary friends in the past, or have very active imaginations. These people know what to expect, and know how to go about things. People who expect to physically hear a voice in their ears, or who expect a dæmon to pop into existence fully formed are often frustrated, and doubtful. They ask "I thought I had found my dæmon, but now I think I was just talking to myself". Well, your dæmon IS yourself - just the subconscious, suppressed side. So obviously he or she is going to sound a lot like you. As you get to know this side of yourself, a gender (often the opposite to your own) and a personality will begin to come clear. You dæmon may try different animal forms until it finds one that is comfortable for it. The Daemon Page has an excellent section analyzing different forms.
You will probably find at first that you are best able to picture and listen to your dæmon during quiet times, when you are alone. One of the best things you can do to strengthen the connection between you and your dæmon is to start projecting your dæmon when you are busy doing things, or interacting with people. He or she may surprise you. Many dæmians say that their dæmon often comments on things other people say and do, answering rude customers sarcastically or making a silly joke out of something a friend has done. They end up suppressing laughter because of a silent comment made in their head.
Try watching TV with your dæmon. What does he or she think of the characters? You may discover that your dæmon likes a character that you dislike, and defends him, or dislikes a movie you enjoy, and expounds on why. This is because some part of your subconscious feels this way. This is the joy of the duality of human nature. Enjoy it!
Dæmians are all different, and may find that different strategies help them get in touch with their dæmon. Some find that free thought writing works well - they try writing from their own, and then their dæmon's voice. Visual people may find that trying to draw their dæmon brings them closer, and helps them visualize. Kinesthetic people may want to try turning on some music while alone and dancing, while imagining an animal dancing too - a bird swooping, a dog shaking its head to the beat. Auditory people may want just to focus on the voice.
Don't pressure yourself too much. If you are not a visual person, don't stress yourself out trying to project your dæmon. Many dæmians say they "hear" and talk to their dæmon frequently, but rarely actually picture the daemon. Others say they can see their dæmon, but that he or she doesn't talk very much. This is YOUR soul. You can interact with it in whatever way you feel comfortable.