So, before I go into what I am talking about, let me give you an example that kind of illuminates the problem. It is a common example for this, and I'll say why I used it after. So, the situation. You're playing in a game, and you are confronted with a locked door. The locked door has a puzzle on it to open it up, it is an intricate puzzle that involves complex thinking and logic to get by. So now, what are your possible solutions to this problem? The "rogue" can pick the lock, but there is no lock just the puzzle. The "fighter" can break down the door, but the door is thick steel so that is out. The "wizard" can magic the door, but there is an anti-magic bubble. So I guess you're stuck with solving the puzzle, right? Wrong.
What is the actual problem here? It isn't the door, it isn't the puzzle, and it isn't that the GM is being an ass hat. The problem here is that you need to get to the other side of the door. So, how do you solve that problem? The door is insurmountable without solving the puzzle, sure. What about the walls? How about interplanar travel? If the walls are stone, I bet you could pull out a block to slip through. The mage could make someone ethereal for a round. There are a lot of ways to solve the problem of "How do I get into that area", but only a few to "How do I open the door".
This very problem is addressed in one of the first episodes of Burn Notice. Michael Weston needs to deal with a guy, and the guy has greatly improved the security of his door. Michael smiles, and then explains to the audience that even a moron will soup up their door, but most of the time they don't fix up their walls. Making the wall the easiest way to actually get the guy.
Now, this is a very simple (and common) example, but it is one to think about when you are playing. Don't think about the problem that the GM has given you, instead boil the problem down to its simplest and truest form. It is not "A door is in my way" it is "I need into that room". It's not "This trap needs to be disarmed." it is "That thing is going to kill us".
Once you know what the problem is, take stock of your resources. What do you have to use? No, not just on your character sheet, the whole thing. Is someone in the room with you? That's an asset. Even if they're an opponent, they can still be used. This is where true creativity comes in though, finding ways to use those things that are not considered by most people to be usable. So let me just say straight off, almost anything can be used to your advantage.
Another example? You're trapped in the classic trap, the pit and the pendulum. You're bolted down to a table, and a blade on a pendulum is slowly lowering closer and closer towards you. You are bound tight to the table, the table is solid stone, and you can't worm your way free. totally screwed? Wrong. So, what is the problem here? "The pendulum blade is going to cut me in half" right? No, the problem is "someone is trying to kill me with a pendulum blade". Why? Well, you didn't get bound to that stone table that well all by yourself now did you? So who put you there? Probably the person you were going after before hand. What do you know about them? What do you have that maybe they could want? Think about it, and think fast, after all the real problem here (despite what I said before) isn't that the blade is going to kill you, it is that you only have X amount of time to make something happen or that person is going to have killed you.
So, find something, and use it. "Wait, I'll talk. I can help you, I know where
So, the next time you find yourself in a tight situation take a second to look at it, and ask yourself "What is the real problem here?" You might be surprised at what you come up with, and the solutions that that brings to your mind.