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The Torah is the five books of Moses. It's what's written on the scroll that Jews read from in synagogue.
That is called the "written Torah". It was transmitted orally until Ezra's time.
The rest of the revelation at Sinai was not written down at that time. It continued to be passed on orally, and is called the "oral Torah". This was eventually written down in the Mishna during the Babylonian Exile.
The Talmud is made up of the Mishna and the Gemara. The Gemora is a collection of commentaries on the Mishna.
On a page of the Talmud, there is the Mishna page in the middle, with the Gemara and the commentaries all around it.
(This can get confusing, especially when someone refers to something "written in the oral Torah.")
Another word you might want is the Tanach.
The word "Tanach" is a three-letter acronym in Hebrew. (Only the consonants count, and the "ch" is one Hebrew letter.)
The "T" in Tanach stands for the Torah, which is another name for "the Five Books of Moses." That's what's written inside a Torah scroll.
The "N" in Tanach stands for "Neveim", the Hebrew word for "Prophets". This is the collection of books in the Bible about the lives of the prophets. (for example, "Joshua" and "Jeremiah.")
The "Ch" in Tanach stands for "Ketuvim", the Hebrew word for "Writings". This is collection of books in the Bible that has the poetry writings ("Psalms", "Proverbs", "Job") the scrolls ("Esther", "Lamentations", "Ruth", "Song of Songs", and "Ecclesiastes"), and a few others (e.g. "Daniel" and "Chronicles")
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Something else needed to fully understand the Torah is the Midrash. (http://en.wikipedia.org/wiki/Midrash )
There are many very important later commentaries on the Torah that are fundmamental to understanding it. Rashi, Onkelus (author of Targum), the Rashbam, the Ramban (Nachmonides), and Ibn Ezra come first to mind.
These are all available in the Mikraot Gedolot, which is a version of the Torah/Tanach with all these commentaries surrounding the text. http://en.wikipedia.org/wiki/Mikraot_Gedolot
Rashi is from the 11th century b.c.e. and is probably the most important commentary for understanding the plain meaning of the Torah text. http://en.wikipedia.org/wiki/Rashi
Rambam's (Maimonides) Mishne Torah is another fundamentally important text for understanding how the words of the Torah connect with the commandments. (Not to be confused with "Mishna")
http://en.wikipedia.org/wiki/Mishne_Torah (12th century b.c.e.)
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There is also the Arba Tumim (http://en.wikipedia.org/wiki/Arba%27ah_Turim) and the Shulchan Aruch (http://en.wikipedia.org/wiki/Shulchan_Aruch) but these are for advanced study.
(This is not to be confused with the "Kitzur Shulchan Aruch" by Rabbi Granzfried in 19th century Hungary, which is not universally accepted and often harsh, but still an important summary/handbook. http://en.wikipedia.org/wiki/Shlomo_Ganzfried Many people quote obscure and harsh rulings from the Kitzur Shulchan Aruch as though these practices were universally accepted. They're not.)
A summary of these is in the Mishna brura (not to be confused with the Misnah or Rambam's Mishna Torah) which is the Chofetz Chaim's summary of the Shulchan Aruch, and helps clarify how Jewish law is applied. (http://en.wikipedia.org/wiki/Mishna_Brura) It is considered authoritative and reliable by many ashkenazim.
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EDIT: In response to "Are there even more things require to full understand the Torah?" I left out something important:
A study partner!
We learn by interacting with the text, not just reading it. In order to do this, you need someone else with whom to study.
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