The man of steel is impossible. Let's not pretend otherwise. The guy has X-Ray vision. He has super strength. He has supercold breath. He goddamn flies. There is no way he could do all that. But if there were, here's how they would work — according to what we currently know about the laws of physics.
Negative mass has never been observed and most likely never will be observed. However, if it were, you would be able to ride it to work one day.