Experience

Player vs. Character
"Challenge a player's skill, not his character sheet." says George Strayton in The Secret Fire. Tabletop role-playing games can do either. I have heard arguments in favor of both sides. Some players seem to prefer rolling against a number on the character sheet, others seem to prefer role-playing out the attempt to persuade the guards. Experience is how we level-up the character and make them better, but experience is also what happens to us as gamers the more we play the game.
As a referee I like to encourage people to role-play an in-game situation, partly because it is way more entertaining to me and the other players than consulting the character sheet and rolling a die. The more we play, the better our play becomes and the more we role-play the better we become at playing roles. The best advice I can give new players is to listen to the description and try to imagine yourself in the situation. Ask yourself "What would I do?" Eventually, you will get to the point you will ask yourself "What would my character do?"
Ask the referee, "What do I see?" a lot. Use your "I"s (play on words here!). Ingenuity; imagination; intuition; initiative; innovation; insight; improvisation; intelligence; information; investigate. Playing a game like Call of Cthulhu is good experience for all role-players because the game demands investigative skills. Ask around, gather information before you decide how to proceed. Use of those investigative player skills comes in very handy while playing fantasy RPGs as well. I encourage my players to make use of their teachers, mentors and sages; to visit the temples and libraries; to ask questions of the NPCs.
One style of play assumes the heroes will be able to stomp any challenge the referee throws their way. That seems unrealistic to me and I have a hard time with the verisimilitude of a game run this way. It seems much more believable that there are things out there beyond our abilities. Fear of failure should not be debilitating, but it should be in the back of a players mind. It adds some suspense and keeps the game challenging.
Knowing when to fight and when to run is one of those player "skills" that will come from interacting in a more realistic milieu with all levels of challenge. Working one's way up to being able to face a bad guy you once had to run from is high drama in my book. It's a "coming of age" story, which seems an appropriate theme given the assumptions of the game. Achieving mastery is a fundamentally satisfying experience. Why should we limit that to the character? Players should have the sense of mastery achieved through skillful play. It can be more than just rolling the dice well.