How can I learn not to get screwed over and screw other people over?

The question suggests a student is asking this question, so I will tailor my response to a school environment. Although there are some social commonalities between schools and large corporations, the general advice I would give is "find better people with whom to associate and do business." I think that the most useful advice I can offer is to focus on the long game. Building credibility is way more important than taking credit. Do whatever you can to help your teams do great work. Over time and different experiences, people will take note that projects where you are present tend to yield better results (they do, right?) and that teams with the people whose work ethic you question generally get poorer results. There's a lot more interpersonal things you can do to communicate your frustrations to the "credit takers." The book Difficult Conversations might be a good place to start. http://www.amazon.com/Difficult-Conversations-Discuss-What-Matters/dp/0143118447/ref=sr_1_1?ie=UTF8&qid=1334697435&sr=8-1

Great answers here, but I have one more thing to add.  Look at the behavior you described (screwing people) as a contagious disease that you don't want to catch. If you neither respect those people nor like them, why would you want to BE like them?  Don't you want to like and respect yourself? Your integrity is more important than any battle.  I think your friends are right: your first step is to learn how to stand up for yourself and project confidence, so that you won't be a target for these people.  (Learning not to be "too soft" is something I'm working on, too.)  The problem with coming across as soft is that it can make you a target.

Pick up a copy of "The Art of Deception" by Nicholas Capaldi.  http://www.amazon.com/The-Art-Deception-Introduction-Critical/dp/159102532X/ref=la_B000APOV8W_1_1?ie=UTF8&qid=1340528689&sr=1-1 It'll help you not to get screwed over.  How you use the information beyond that is between you and your mirror.

First of all let me say there is nothing bad about what you want to achieve. People might tell you otherwise, but they are either playing the game or don't understand it. To get you started I suggest you read the following book very carefully: http://www.amazon.com/The-Laws-Power-Robert-Greene/dp/0140280197 It contains pretty much all the theoretical knowledge that you need. After that it is mostly practice and the ability to analyse situations, reading people, and to be able to distance yourself from people. Probably the most important rule is a combination of always appear to be nice and never attack directly. Instead of, for example, confronting someone directly make sure that, when third parties are present, you say something like: 'I am glad that you could make good use of my paper when presenting it to X' - that's obviously situation dependent, but you need to assert a social dominance over the other party without being aggressive or opening an attack surface yourself. You might also want to watch this years Celebrity Apprentice, Aubrey O'Day is doing a fine job. It is also worth watching the former Miss Universe, who knows exactly when to shut up and let others dig their own graves. That said you also need to understand yourself. Everyone has good and bad days, and it is important that you avoid confrontations on bad days because there is a higher probability that you will lose. Some people suggest that being nice and praise others will come back to you in a positive way. I found that to be true when working in high growth industries, where the pie is growing and it makes more sense to have allies. However, in most industries there is a fixed size pie that multiple parties compete for. Nice does not work there, and in fact nice will get you thrown under the bus.

Oh wow. So what you're saying is they stole all your credit and then pointed at your angry reactions like that was just more proof you weren't very focussed? I mean, that they were so self involved, so insecure and so desperate to get some credit somewhere, that they took what was due to you, regardless of how much it meant to you? And then, because they are all about 'how it looks', they couldn't or wouldn't engage with your honest reaction, leaving you feeling even more isolated? Wow, sucks to be them, I mean, that level of personal insecurity requires a constant stream of intelligent friends to steal from, to anger, and to ultimately lose and I wonder how they're going to cope in a dry spell, or in an exam. I wonder how much of this amazing life they miss, from having to stay targeted on where their next cheating move could be. Sounds like you are already better off than them, because you have escaped being that needy.  When you come across people like that, the nearest place to look for friends, I guess, would be amongst those who dropped out of favour just before you turned up - they likely have the same goals as you, as well as the same insight - especially if they acquired that the hard way.