Politics within the camarilla can be an extremely difficult thing to comprehend, on some levels it mirrors mortal systems of democracy, mixed with a splash of dictatorship. How much pull and authority a primogen council, and by extent the prince largely depends upon the individuals in question. Every city will have differences, and neonates often have the daunting task upon entering a city - that is, learning how the city politics work and how to avoid trouble within the system.
Here, I have outlined the basic principles of the primogen council, princes, and city politics, mainly gleaned from the White Wolf Sourcebook: "Counsel of Primogen". Even if you do not play a high roller in the world of darkness, the information can help you understand your rights (or lack thereof) and your place in a largely unfair society.