My personal rules for organizational behavior (not all directly applicable to the particular situation you mentioned, but it seemed you wanted general advice not just specific advice):
Rule 1 (and the most important) - never let your boss be blindsided because you didn't give him information about a potential problem. This means add him to the email chain (any potential problem generally has one) or forward past emails he wasn't copied on. And if the issue has the potential to be really big (or to come to him from someone above him) or there is no email chain, go tell him in person.
Rule 2 - know who the goto people are for various things you will need. Help them out when they need it.
Rule 3 - Never let another employee know you dislike them. Be polite and friendly to everyone.
Rule 4 - Ask for things through the informal chain first where possible - then followup with the official request. So you tell your boss you are going to need this person and why and get his general agreement. You call the person's boss (or better yet have the boss do it) and tell him the problem and get his general agreement and tell him to expect an offical request. Then you put in the request in writing.
Rule 5 - When possible go to management with a potential solution as well as the problem. And where possible fill out any required forms or paperwork for them (you may want an informal agreement to the solution before you do this) so that all they have to do is sign.
Rule 6 - You don't get what you don't ask for.
Rule 7 - Learn the politics of the office. If George can alawys get things done, get George on your side before a major meeting or get him to help with a request that might be hard to sell (unless your boss hates George - in politics it is generally better to err on the side of your own boss unless you know positively he is being removed). This will probably also involve helping George out when he wants something or needs help. Politics is very much about favors for favors.
Rule 8 - If there is a major political war going on in your office, stay out of it as much as possible. People who aren't in positions of high power can never win by getting involved in these things.
Rule 9 - Have something to trade. Be the goto person for something.
Rule 10 - Get to know people. Ask about their families, express condolences when they have a death in the family. If you know he is a Giants fan and the Giants just won the Superbowl, then make sure to stop by and comment on it. Share some of your interests with them. People work better with people they like.
Thought of a couple more.
Rule 11 - When people are overwhelmed (this is when they are seriously overwhelmed due to an unexpected occurance like a subordinate going on emergency leave or they need to drop everything and meet a deadline becasue someone else failed to get the stuff done), volunteer to help if they are in your work group or one of your immediate bosses. This one is tricky because you don't want to do it so often they think you have no work to do and because you can't let your own work not get done because you are helping someone else. And when you do this, you may need to stay a little later to ensure your tasks don't get behind schedule. If you are asked to pick up someone else's work because they are in the hospital or on Emergency leave, do it graciously and without complaining about the state it was in (your stuff isn't perfect when it's not finished either).
Rule 12 - Present things to management in busness terms. You will go a lot farther getting things you want done if you can express them in terms of increased income, decreased costs, or client satisfaction.
I'm an introvert and I can do these things, so even if they don't come naturally to you (they don't to me), believe that you can do them.