The first step is always the hardest and the most drastic step. Whenever that particular annoying person is within your vicinity or the gathering you are a part of, remove yourself from there. Staying away and getting away from such people is the perfect way to ignore them at first. If that particular person is a stranger, simply do not respond.
Try to avoid discussing matters with these people. At times such people are present in places where it becomes an obligation to sit in their company, for instance your workplace. In such cases, you should not respond to the remarks that the other person makes. Try to remain silent and do not discuss anything with them.
Sometimes all you need is an open space in order to concentrate your thoughts and to let out your anger. If you are in an office meeting where the other person is constantly bugging you, simply make an excuse and go to a restroom. Take a deep breath and set focus on the right thing and not what this other person has to say.
Always remain in control of conversations. Try to avoid the other person at any cost. If the other person intervene in your conversation, always remain focused and take back the control you believe you are losing.
Always be patient and professional. That is the key to avoiding people and ignoring them. Pretend as if they do not even exist.
Always remain focused on things you want to achieve and not what the other person has to say about you. It is useless to waste your time and energy on an imaginary dialogue with this person.
If you do want to imagine things, then do not imagine that person in a fight of words with you, but in fact imagine that person being extremely harmless to you.