"I want to learn Japanese" is 日本語を習いたいです in Japanese. にほんごをならいたいです。(Nihongo wo naraitai desu"

There are several ways of saying, however, the basic one we generally use is 日本語を勉強したいです like "want to study". The other ways of saying are, as Brian and Nick said, ならいたいです(learn with/from someone or professional teacher) and おぼえたいです(like "study memoraizing"). You can also say 日本語を身につけたいです(like "want to have the skill of Japanese language"). I hope this helps you.