Tarawih is a sunnah mu'akkadah - meaning a verified sunnah that the Prophet used to do consistently. He technically used to pray qiyaam al-layl (optional nightly prayers) year-round, out of devotion to Allah. It must be clarified that tarawih is essentially considered qiyam, but it was given the name tarawih - which literally means "to rest and relax" - in reference to how the sahabah (companions of the Prophet) and righteous used to literally rest every four raka'as because of how lengthy the prayer was.
This book presents step by step how to pray Taraweeh prayers