OK, if I woke up with a super power...
I live in an extremely suburban area so I couldn't just find a crime by swinging/flying around. I'd kinda have to move somewhere closer to work (and with a larger number of people who don't hate comics). I guess I'd help people but only if I got some serious powers. I'd be scared to death if I had to fight crime as Shadowcat or Mr. Fantastic (except stupider) or something. If I were more like Spider-Man or Superman I'd do my part but wouldn't make a profession out of it. Aside from that I'd tell a trusted inner circle and have fun (in the web-swinging around sense, not in the above the law sense.)
I'm thinking this is a hard question to answer. My first instinct would be to test my limits, but then that depends on what the power is that I've gained. For instance, if it was the power of flight I wouldn't start flying around because the power could just give out and I'd fall out of the sky. If I was able to be intangible I don't think I'd start walking through walls and take the chance of being stuck halfway through. So I'd be really cautious about the use of my powers for awhile.
And I don't think I'd tell anybody about my powers, because I wouldn't want people calling or knocking on my door 24/7 asking me to use my powers for their benefit. "Hey can you fly up and adjust my satellite dish?" or "I locked my keys in my car. Can you reach through the door and open it?"
Another problem with telling people would be the loss of privacy. It would be instant celebrity status, only worse because there's nobody else out there who can do what you do. You'd be living in a fishbowl.
So I guess if I ever did wake up with a super power I'd have to start wearing glasses to hide my secret identity.