This will apply if you're using a Windows system, and be most accurate on XP:
If you're already able to view Japanese characters then you're most likely already half way there.
Go to your control panel.
Find Regional and Language options.
Click the Languages tab.
Be sure the "Install files for East Asian language" checkbox is checked. (If it's not you'll need your Windows CD to install them)
Click the "details" button under Text service and input language.
The Text service and input device window should now be opened.
Go to the Installed services area and click "Add"
Find Japanese in the Input language.
It's best to use the default Keyboard layout/IME that will be selected most likely. (This is Microsoft IME standard 2002 ver. 8.1 for me)
Click "OK" and the language should be added (You may need to be reboot, I don't quite remember)
Once you're done, you should have access to a language bar which you can switch between input languages. Select Japanese, then select the kana and begin typing in Romaji. The characters should be automatically shifted to the kana, and at the end of a word you can hit space to select the appropriate Kanji to replace the kana.
Some keyboard shortcuts:
Changing Input Language: Shift + Alt
Katakana: Shift + caps lock (Only while Japanese language is active)
Hiragana: Ctrl + caps lock (Only while Japanese language is active)
Toggle between last Kana and direct input: Alt + ~ (Only while Japanese language is active)