* lernen is the general term for studying, learning, or studying something. For example, "Ich lerne Deutsch" means "I am learning German."
* studieren specifically refers to studying at a university or other higher education institution. For example, "Ich studiere Medizin" means "I am studying medicine."
So, if you're talking about studying in school generally, use lernen. If you're talking about university studies, use studieren.