To learn how to read & write in Japanese, the other replies gave you some good web sites to get some basic language instruction. However, if you are asking how to be able to write Japanes on your PC, you may need different kind of help.
First, are you living in Japan? I need to know if you have easy access to Japanese software. What kind of PC and operating system are you using? There maybe some very easy solutions, if you are using Windows 2000 or XP, or even Windows 98.
Office XP will allow you to type in Japanese script (as well as many others), unfortunetly the proper fonts don't come pre-installed, in fact they arent even on the CD, you'll have to go to Microsoft's website (Microsoft - Official Home Page) and go to office updates, you may need to do some searching.
if you're on 8.5 and above the CD should have it. Prior require Japanese Language Kit (JLK) which wasn't too bad.
OSX allows almost any language install easily with the main CD ... But then again I bought my copy at Yodobashi Camera. The update panel might be able to pull it down. My keeps showing all kinds.
Office XP is probably following Apple's step to allow simple settings change to use other languages. While Apple basically is multi-lingual from the start now.
Apple's greatest drawback is that Kanji choosing is still pretty ignorant. It misses simple names at times and chooses a different character for you. Still not bad but ... some Japanese complain at times. Although, the OS has that slight minor problem Apple has been pushing for a decent Kanji standard.