Japanese consists of three separate writing systems -- a phonetic alphabet for Japanese (hiragana), a phonetic alphabet for foreign loan words (katakana) and a set of characters that represent words (kanji). Learning the two phonetic alphabets first will allow you to write whatever you want in Japanese. Even if you don't use the kanji characters, a native Japanese person will be able to understand what you're writing.
Whether you're learning to write the kana or kanji, it's important to know the order in which you should write the letter. To learn the correct stroke order, you can use a book that teaches Japanese writing, flash cards that contain stroke orders or websites to help you learn to write in Japanese. Once you have mastered the order of strokes, you just need to practice writing each letter.
Genkoyoushi is a special type of paper that Japanese students use when learning to write. It is a graphing paper with large squares that have smaller squares inside. Write each character in a large square, using the smaller block as a guide for getting the scale correct. You can purchase this paper at Japanese specialty stores in your town or online.
Becoming a fluent Japanese writer requires practice every day. Keeping a journal helps you to practice not only your writing, but also your vocabulary and grammar. If you don't know the kanji for a word, you can write it out in hiragana. As your knowledge improves, you can begin to incorporate more of the kanji into your writing.