Most of your general help needs can be answered by the help pages at the wikimedia meta-wiki: http://meta.wikimedia.org/wiki/Help:Editor .
Here's a short summary of some typical actions.
To create a page, search for it by title. This will make sure that you aren't overwriting an existing page. If the search fails (as is likely), the search page will give you the option of creating and editing the new page. Take that option.
To place a page in a Category, add [[Category:name]] to the page that you are editing. E.g., [[Category:Design_Documents]].
Document creation in a wiki is apparently bottom up: pages are created, then organized by placing them into categories or by establishing links between them. Thus, you cannot add a page to a category from the wiki page that displays the contents of that category; instead, you must create the page (using the search approach) and then specify to which categories it belongs. One advantage to this approach is that very general relationships between pages can be expressed, not just hierarchical ones.