If you do something incredulously, you're doing it in a doubting or disbelieving way. If you look at someone incredulously, you can't believe what they're saying or doing.
Incredulously is a word that has to do with disbelief — it's a way of looking at someone or talking to someone like you just can't believe what's going on. If your teacher suddenly started quacking like a duck, the class would look at him incredulously. When a student gives the wrong answer to an easy question, the teacher might incredulously say, "What?" If you're feeling incredulous (disbelieving), then you're probably acting incredulously.