What is the difference between
De Nada and
No es problema? They both mean "no problem", or "it was nothing", right?
"De nada": It means like "you're welcome". When someone makes you a favor or provide help, you say him thanks (gracias), and then he responds with "de nada".
"No problema": It's quite similar, the difference is that "No problema" is usually used before someone makes the favor, or give help.
Gracias por ayudarme con mi tarea. -De nada, fue un placer.
Me puedes recoger del colegio a las 3:00. - Claro, no hay problema.
While "De nada" means "you are welcome", "No problema" is not a correct sentence in Spanish.
The correct way of using the second sentence would be: "No hay problema" or "No es problema" which literally translates into "No problem" and "it's not a problem" respectively.
Other than that, the difference between using one or another was well explained in the answer provided by @Nicolas.
Having lived three years in Mexico, I heard both "de nada" and "por nada" used for the English "you're welcome". "De" can mean either "from" or "of", while "por" means "for".
Things do not always translate literally between languages, but think of both of these as meaning "It was nothing", or "Don't mention it" in English.
Also, think of the poor Spanish speaker learning English, trying to figure out why they shouldn't mention something!