This is just a cheat sheet, so this will be brief and sketchy until somebody fleshes it out.
0. You need an account. The wiki uses separate user accounts, so you cannot use your Nekochan forum account.
1. Click on the "log in" link at the top right of a page.
2a. In the dialog box, click on the "request one" link if you don't have an account yet.
2b. Enter your username and password, and login. You'll be returned to the page you were viewing, but you'll see your name and some other links at the top right of the page.
3. To edit an existing page, once you're logged in you can go to that page and use the "edit" tab at the top of the page.
4. You'll see a text editing box in the resulting web page, and the page content including the wiki markup.
5. Edit the page contents.
6. Enter a summary of your pages in the cleverly named "Summary" text box below the editing system.
7. If you made a minor correction to the page, check the "this is a minor edit" checkbox.
8. If you want to get email every time this page is changed, click on the "Watch this page" checkbox.
9. If you're happy with everything, click on "Save page."
10. If this was all a horrible mistake, click on the blue "Cancel" link to the right of the "Show changes" button.