How do YOU (yes you) debug a program?

You've just coded a sweet new algorithm that takes a string and some some fancy business on it, or maybe a new hashtable, controller, or SQL function...

But the function is not performing how you expected...

What do you do? Walk us through your process.

Do you use a debugger? Do you use log/print statements? Which area of the code do you look at first, second, third?

I think it will be a lot of fun to share each others' debugging tips.