Japanese have 3 type of writing style - Hiragana, Katakana and Kanji.
To start off, most non-native Japanese will learn Hiragana 1st before moving on to Katakana and Kanji. However, interesting to note that most native Japanese might start off learning Katakana and Hiragana at the same time during their kindergarden days.
Hiragana - 平仮名(ひらがな)
Hiragana is the basic form of writing Japanese similar to English basic A-B-C
Example : a, i, u, e, o (あ, い, う, え, お).
To form a word, you need to join the hiragana together like the sentence "I am ____ " - "watashi wa ____." (わたし は _____ です。)
Katakana - カタカナ(かたかな)
Katakana is the writing style for foreign object/names like camera カメラ.
Example : a, i, u, e, o (ア,イ,ウ,エ,オ).
Generally, items that is imported into Japan are adopted using Katakan like
ラメン - ramen (China),
パン - pan (means bread in French),
アルバイト - arubaito (Arbeit means part time job in German).
Foreigners learning Japanese, generally write their name in Katakana.
Kanji - 漢字(かんじ)
Kanji is the Chinese character writing style that migrate from China to Japan
Example : watashi - 私 (also can be written in hiragana as わたし as a break down for people who don't understand Kanji). Generally, Kanji is a set of words form from hiragana.
Furigana - 振り仮名(ふりがな)
Japanese generally write their name in Kanji with same hirgana above or below to aid with pronouncation as Kanji might have multiple pronouncation. The same hiragana used for reading aid is known as furigana.
Kanji vs Chinese Characters
A lot of people ask this on Yahoo Answers where I used to be very active in giving out answers and asking questions. I also posed this same question to my 1st sensei before on the difference on Chinese characters and Kanji.
As far as I understand, Kanji and Chinese characters have up to 70% similarity in meanings. Meaning a Chinese might be able to understand Japanese without learning Japanese! However, some Kanji have totally different meaning to their Chinese counterparts. For example, Kanji characters like 勉強(べんきょう) means study but same Chinese characters means compel!
Therefore, it is still advisable for Chinese students who are learning Japanese to be able to differentiate the meanings to avoid confusion.
Romanji ロマン字（ろまんじ）
Most non native Japanese learners started off with Romanji, which is the English alphabets of the Japanese pronouncement. However, it is strongly to recommend one to move off to Hiragana and Katakana as soon as possible. In most Japanese language school, sensei (Japanese teacher) will only use Romanji during Elementary class and will drop almost entirely of Romanji by the end of the course.
Hope with this mini explanation of Japanese writing system, you can understand Japanese better!!!
Cya and stay tune for my 1st Grammer lesson in Japanese!!! (^u^)'')
Japan - 
China - 
S.Korea - 
Singapore - 
Malaysia - 
Indonesia - 
Russia - 
Germany - 
Italy - 
France - 
Britian - 
Spain - 
Portugal - 
Greece - 
Turkey - 
Eygpt - 
Australia - 
New Zealand - 
U.S.A - 
Canada - 
Mexico - 
Brazil -