There are three key individuals/group you should focus on initially:
- The Lynchpin - This is that person involved with just about all the basic workings of the company. It could be the receptionist, someone's assistant, the office manager or even a janitor (It you're a teacher, you'll know what I mean.). Be nice to this person. Don't even think about looking down on them. If they really wanted to, they could make your life Hell.
- Your Supervisor - Did deep and get to know what your boss really expects out of you. If he wants things done fast at the expense of a little sloppiness, work a little faster than you would like. Know which projects take priority. When you're valuable to your boss, he will fight to keep you and bring you along as he gets promoted. Don't even think of trying to make this person look like a failure. You'll regret it.
- Your Team - Get along and make every effort to contribute. Do a little extra. Volunteer occasionally for one of those tasks everyone hates. It's not that you have to get on the good side of any one of these people, but you want some type of consensus that you're good for the team.
Without making these solid connections, it will be counterproductive to try and focus too much on other department heads or the CEO. Those relationships will take time and are a lot more productive when you get positive comments from the big 3.
You may discover that your boss is not affective at office politics either. This is a problem because you need him. If there is a chance to move to a more strategic area, take that opportunity.
Also think about advancement inside or outside the company if you must. It is difficult to be influential in any organization of you're not seen as successful. We don't like to admit it, but money talks. If you're willing to low-ball you value to the company, others will as well. Know what you're worth and don't be afraid to be paid accordingly.
Many companies have social occasions. If people meet outside of work, get involved. Don't eat lunch alone. Help pull others out of their shell. It's human nature that people will like you the more they get to know you. It builds trust.