In many cases, a person needs a rabbi who knows their personal situation in order to render a psak in certain big life questions. And a good rabbi does more than just give rulings, he also gives personal guidance in life. (For this you need to find a rabbi who is not only competent, but also "gets" you.)
Generally you will follow this rabbi's rulings. But one also can ask other rabbis, esp. about day-to-day stuff that comes up. Rabbis tend to be busy, and you might not be able to get your rabbi on the phone immediately. When a ruling becomes binding is its own subject. Generally once you ask a Rabbi and get a ruling that is binding. You can ask your primary rabbi if a ruling you got is binding or not.
Sometimes one has to consult different rabbis in areas that require expertise. A good rabbi will tell you when you need to go to someone else. And for advice, you can consult as many people as you want.