Answering a phone at work is an entirely different matter than answering a call at home. At home you usually answer calls from friends and family and depending on your mood. At work you need to act like a professional. This means leaving all of your personal problems at home and answering the phone in the most courteous and helpful manner possible.
First thing you need to do is to train yourself to pick up the phone as soon as it rings. If you cant do this, have a back up available that will be able to. Not answering the phone can give the customer the impression that you dont care about them and their needs. Greet someone on the phone as if you are meeting him or her for the first time and want to leave the best impression possible. Young people usually do this on first dates when they meet the girls parents and want them to approve of them. The only way that is happening is if you act mature and understanding. They are looking for someone who is responsible. When you answer the phone try to answer like someone who is happy to speak to someone and genuinely want to help him or her. People can easily spot fakes so dont try to say things that you dont mean.
After you greet them, if you find that they want to speak to someone else, ask them, do not tell them, if they can hold on a second while you check on that person. If the person is unavailable, offer to help yourself or ask them if they would like to speak to someone else who is qualified to help them. If they approve, check that that person is available before transferring the phone. People hate to hold on the line only to find out the person is not there by listening to their voicemail. They may wind up feeling cheated and betrayed.
Remember that this maybe their first time calling and if they dont receive satisfactory treatment, you may in fact lose that customer. With the power of the word of mouth, you may wind up losing more than one from a single phone mishap. So brush up on your telephone answering skills and always treat callers with respect.