You just need to install an input method framework and a Japanese language backend.
I've personally been using scim for the framework, but some recent comments I've read seem to indicate that it's kinda on the way out. uim is also a good option, but I personally don't like the toolbar interface much. There's also ibus, a relatively new one that looks promising, and which I believe RedHat based distros are using.
For the backend, anthy seems to be the most-used, but there's also prime and maybe one or two others. You need to install the package designed for your framework, something like scim-anthy or uim-anthy.
Once you have everything installed, you can use im-switch to set it up. This also allows you to have multiple frameworks installed and to switch between them easily.
This page has a good general rundown on linux text support:
Edit: Whups, just noticed you said you're using Easy Peasy. I'm not sure how well this relates to such netbook systems. Hopefully it will still apply.