For this section, I'm assuming two things. First, that there are well-defined goals for the project. Second, that these goals motivate whatever you are trying to achieve. If one or both of these assumptions isn't true for you, this section will still be of use, but there will be more work for you to do because you'll have less leverage to make things happen.
The process described here makes the most sense for large power issues and for when you are in a situation where you need more power than you have. The bigger the issue, the more faithfully a thought process like this should be applied. The smaller the issue, the more of these steps you can probably speed through or skip altogether.
The only way to be successful in resolving a political problem is to be very clear on what it is you need, and then develop a plan to get it. The common needs are:
Resources (money, time, staff)
The authority to make a decision
Influence on a decision under someone else's authority
Adjustment of others' goals to support or align with yours
Adjustment of your own goals to better align with others'
Advice, expertise, or support
However you define your needs, prepare to be flexible. Even if you decide that the real need is resources, while you are seeking them out, do not stop listening for suggestions from others that satisfy the goals but do not involve acquiring resources. By pushing for a larger budget or more time, you might force ...