How to pronounce the 'c' and 'z'

Aside from Rocket Spanish, I'm also taking a classroom course. In that course, the teacher says 'c' before 'e' or 'i' = 'th', and the letter 'z' has a 'th' sound too. I'm confused. Which one is correct, and which one should I use?

Your teacher is describing the pronunciation used in Spain. In Latin America, the pronunciation is like what you hear in the Rocket Spanish lessons.