There are times when you just need to get one thing done with the help of a bureacracy, quickly, and you don't care how - in which case you might not want to read this note, but How to conquer a bureaucracy instead.
This note is more about how to get along with bureacratic systems over the long haul (and with any bureacracy, that long haul is going to seem longer than it is.) Say, as a professor, employee of government, applicant for a student loan, or in an extreme case, when receiving Welfare or Disability. In the latter case, this may be a life-or-starvation situation for you, and an ongoing one. These cases require a different, and in some cases opposite approach, than rough conquest. You can't just triumph and leave. You can't anger or frustrate or manipulate the system too obviously because you're in a n-repetions game, as the game theorists would say: there will be ample time for payback by the bureacrats and you don't have the power to prevent it or retaliate.
Being "nice" is a great start, particularly if you've got a false smile as bright and wide as J Lo's, still have enough teeth to pull that off, and maybe some artificial breasts. But it's not a question of merely being polite. That's a good idea, but the the guiding principle here is this: always save the bureacrat time and bother, if you possibly can, while making it clear you wish to do this. If it's obvious that you want to save your clerk/attendant/social worker/supervisor/prison guard time and fuss wherever possible, why then, you're a good client. If it's clear you selfishly care more about your own broken leg, festering sores, or dead first-born child than their convenience and coffee-break times - why then, you're a very bad client, indeed. That's the deal, the whole deal, and all the parts of the deal.
So any gamesmanship on your part that causes them the slightest extra work or frustration is extremely ill-advised for a long term relationship. (There's some marital advice here if you can find it.)
Secondarily, it's nice to spare their ego, if at all possible, and to be very careful not to show anger to the person "serving" you. Remember they're trapped in the system, too, and their list of complaints and petty grievances against the way things are probably beggars yours - they just can't state them, at least not to you. Not if they want to keep their job. So make sure your complaints and irritability, if any at all, are always obviously directed toward the system, or the rules, and never to the person who's in front of you - within spitting distance, as it were.
Third, don't assume you'll be told of assistance available to you (or anything else) without asking. Sticking to our welfare or disability example, in Alberta, Canada, when I was a Policy Advisor for the Provincial Government some years ago, it was strictly forbidden for social workers or anyone else to tell destitute or ill clients of programs or money available to them for the asking - in fact, I believe it was actually a firing offence to disclose such information unless the information was specifically requested by the client. The ideal for governments is to have many wonderful programs that no-one actually uses, since actual use costs them money, and that means taxes must be collected, and then they don't get elected again. (Similar budgetary principles apply in most other bureacracies.)
Fourth, be assured that the person serving you has no idea what the actual rules are, no matter how certain they seem of the facts. Ten to one there's a list of exceptions and a couple lists of exceptions to those exceptions to anything they tell you. Before the advent of computers, clerks actually did know the rules, which had to be simple and were therefore almost always harsh and ridiculous. Now, the systems and policies try to seem fairer, and are therefore far too complex for any disinterested clerk to have memorized - although they probably know someone who knows someone who has seen the manual and could probably find it again. The clerks will give you their own, personal, dumbed down version of policy, and do so in reassuring tones of tomb-like certainty. But in almost every case what they say will be incorrect as stated. This creates a dilemma. Walking the clerk through the logic of the system they've just described step by step will likely prove to both of you that they're at least partly wrong, and maybe just out to lunch, but the loss of face will likely win you a mortal enemy at the same time. What to do? Trying another clerk another day might work, finding an advocacy organization (there are many, and they rock) is another approach. In the moment: expressing puzzlement and confusion about a contentious point is another effecive tactic if not overused, as this reassures and slightly flatters the clerk. It also gives them time to realize that what they just said is contradictory or can't be quite right, along with permission to change their mind about policy since you're gosh-so-confused you probably won't notice them backtracking, anyway. Don't do this too much though, as this eventually might cause the clerk to speak to you v-e-r-y s-l-o-w-l-y and waste everyone's time.
In sum, always feel free to rely on the self-interest of those who serve you, and be aware right from the get-go that all power disparities are inherently abusive (there, I've saved you the trouble of reading Hegel in translation.) So, of course you'll be abused and humiliated. That goes without saying. The question is, will you get what you need at the end of the day? Be a good boy or girl (or professor or clerk or supplicant) and you probably will.