Most people avoid using the word politics when speaking of their job. The fact is, though, that polishing and exercising one's political skill is crucial to success, especially in dealing with stakeholders. The project manager's influence in an organization can be fragile at best, but exercising his political skill is one way to build influence.
In his book on project management, J. Davidson Frame defines a three-step process that a good project politician follows: 
Assess the environment. The environment of the organization is determined by the corporate culture, so the project manager must be sensitive to the corporate goals and strategies and who the relevant stakeholders are.
Identify the goals of the principal actors. Making sure the project goals are consistent with those of the stakeholders is the surest way a project manager can obtain and keep them as allies. To understand a stakeholder's goals means asking: "What drives this person? Does she have a hidden agenda? If so, how can I deal with this hidden agenda?"
Assess your own capabilities. Successful project managers know their own strengths and weaknesses and how best to capitalize on their strengths. Once the project manager identifies the stakeholders and their goals, he has to act to mitigate any negative feelings or reservations about supporting the project.
These three steps—assessing the environment, identifying the goals, and assessing your own capabilities—are the basis of increasing political awareness about the culture in the organization, and is one way to increase your influence in the company.
Credibility means that the project manager is known to be a person of integrity, knowledgeable, capable, and dependable. A reputation for credibility is earned; it cannot be established overnight, and it will not be believed until it is demonstrated. This quality is something that the project manager must work at with patience and persistence. The only way to be credible is to deliver as promised, be honest in all dealings, and be consistent in behavior.
Almost every other mistake a person makes can be overcome and forgiven—but not dishonesty. Once a person lies, no one fully trusts her again, and her credibility disappears.
Ethical behavior has become so important in project management that the Project Management Institute (PMI) requires every PMI member to sign a Project Management Code of Ethics. In fact, one of the surest and fastest ways for a Project Management Professional (PMP) to lose her certification is to exhibit unethical behavior.
Ethical behavior simply defined means to do what's right. Yet, many professional project managers will risk damaging their credibility and violate their ethics rather than admit that they are having a problem with a project. This is a serious failing.
A major problem, though, is that the project manager is sometimes caught in the difficult situation of being directed by a senior manager not to reveal a problem to a customer. The rationale is that the problem will be corrected without the customer's ever being the wiser. In this situation, you have to evaluate your ethical code and decide whether your conscience will allow the lie, and if you are willing to risk your professional reputation.
Certainly some judgment is required about the seriousness of a problem and whether it is a breach of ethics not to inform the customer. Every project suffers daily snags, irritations, and false starts. The customer will not be interested in these problems—they are the normal difficulties encountered in running a project. However, if the problem is severe enough to cause a delay or requires a short-term infusion of additional resources, the customer needs to know about it. The customer will not be upset that the project encounters a problem, but she will be very upset to learn of the problem after it is so big that there is a significant impact on the project. Customers typically accept problems as long as they can be a part of the solution.
J. Davidson Frame, Managing Projects in Organizations, Revised Edition (San Francisco: Jossey-Bass, 1995).