What is the apporach to learning in judiasm? What do you learn first, the language, chumash, gemorah, law, what comes first, what is the order? After you know the proper order, do you learn one subject as deep as you can until you know it all by memory, or do you read it once and continue going with other subjects?

The recommended order of study of Torah is mentioned by the Sages in Pirkei Avot (chapter 5). First Chumash, then Mishna and finally Gemara. The Talmud (Kiddushin 30a.) instructs that a person should divide his Torah study into three parts: Chumash, Mishna and Gemara. Within these very general guidelines there are many other aspects of the Torah; Halacha, Jewish thought, ethics etc. In the Shulchan Aruch (Yoreh De'ah 246:4) the Rema brings the opinion that by studying Talmud one covers all three parts of the Torah. The Bet Yoseph (ad loc.) also offers different explanations to the above Gemara. A child who studies Torah in school from a young age would probably learn things in this order. However, in a case in which somebody has limited time or when one began to study as an adult, priorities would change. (See Shulchan Aruch Harav, Hilchot Talmud Torah 2:1,9) There are additional factors in choosing what to learn. The Gemara says: "A man can learn only (that part of the Torah) which his heart's desires." (Avoda Zara 19a) After having said all that, it is difficult over the internet to offer the best plan of study and one should consult a local Torah scholar with whom he feels comfortable to suggest a custom made plan for Torah study.