For years, Japan had absolutely no writing system whatsoever. When Buddhist monks from China introduced their writing system to the Japanese, they were fascinated by the pictographs and eagerly rushed to adopt them into their own language. Where there was a Japanese word, they took the Chinese character of corresponding meaning and attatched it. Problem: Chinese Grammar and Japanese Grammer are completely different from each other. Chinese is missing the grammatical endings that are used in Japanese. (-ly -ed -ish -ing ect.)
There was also no way to write other words such as is, and, would be, could be, ect.
Therefore, they took some elements out of certain Kanji characters, abbreiviated them, and created KANA, comprised of characters each representing a specific syllable with which to attatch the grammatical endings and write all the in between.
Think of it this way: They could use a single character to represent the word for WRITE but they couldn't use Kanji to represent WRITING or WRITER. This is where kana comes in: For the word WRITING, the WRIT would be in Kanji and the ING would be in kana. Same for WRITER: WRIT is in Kanji, and ER is in kana.
Also, when more than one Kanji character is used together, they form compound words, typically having something to do with their meaning. A famous person, a MEIJIN, is written with the Kanji for NAME and PERSON. The word for Japan, NIHON, is written with the characters for SUN and ORIGIN. The word for navy, is written with the Kanji for OCEAN and MILITARY.
Kanji has multiple readings which change depending on which characters are used along with it. This makes it almost impossible to successfully study all the Kanji needed well until you are near fluent in the language of Japanese. (about 2,000 Kanji characters are needed before you are considered 'literate')
Kana has two systems, Hiragana and Katakana.
Hiragana is used as mentioned above, for grammatical endings and as filler. However, ONLY words of Japanese origin can be written with Hiragana. This is where katakana comes in. Katakana is used to write all words of foreign origin adopted into the Japanese language. (There are many from our language that are used in Japanese every day.)
ANYTHING can be written in kana, so beginners to the language do not need Kanji right away. In Japanese schools, Japanese children are taught first Hiragana, then Katakana, and finally the study Kanji througout the years.
Romaji is simply our alphabet when used to write Japanese words using our written system.
Japanese should NEVER be learned using Romaji. It will cripple and disable you and you will never be a great speaker like you could be. Anyone desiring to learn Japanese should immediately learn Hiragana and Katakana as quickly as possible, then study using those systems only.
Kanji should be fully studied only after getting a good grasp on the language.
For more information on learning Japanese, check out a wonderful site known as
http://www.yesjapan.com
You can not find a better site on the internet for learning to speak, read, write Japanese.