Descartes is famous for his proof of the self- "cogito, ergo sum" or "I think, therefore I am." This seems to be a common sense statement, but I have heard it contested. I have read things from both Russell and Nietzsche stating something along the lines of this: In his statement, Descartes has already assumed that something must think for there to be thinking. Following this logic, one can only say for sure that "there is thinking" and nothing else. I fail to understand how this is plausible. Perhaps it can better be stated "I am conscious, therefore I am", but I fail to see how there can be consciousness without something that is conscious! Also, what would Sartre and Heidegger have to say about this?

Yes, but we know something must be conscious of the thinking, otherwise the thinking would not be perceived. "I am conscious, therefore I am" seems to fit the picture.