There are exactly two things you need in order to contribute to OpenWiki: something worth adding, and the Edit button.
That is the whole process. You do not need an account to do any of it.
Edits made without logging in are credited to Anonymous in the page history. That is the whole of what is recorded — there is no way to type a name into the edit form, because a name nobody owns tells a reader nothing.
Registering an account gives you a name that is yours. Usernames are unique: once Ada is taken, no one else can edit under it, so when a page history says Ada made a change, it means the person holding that account did. Accounts need a username and a password and nothing else — no email address is asked for, which also means a lost password cannot be recovered.
Anonymous edits are not second-class. They appear in recent changes like any other, and are judged the same way: on whether the change improves the article.
Start from Special:WantedPages, pick a red link, and write two or three paragraphs. A short, accurate, well-linked article is far more useful than a long unsourced one. Add {{Stub}} at the top if it is clearly incomplete, and finish with a category.
It goes live immediately. There is no approval queue: this wiki publishes first and reviews afterwards, which is what makes "anyone can edit" true rather than a slogan.
Three things happen around that:
A small number of pages are protected or use pending-changes review. Those are exceptions, applied to pages that attract damage, not the normal state of the encyclopedia.
Other people will change what you wrote. This is not a rejection; it is how the encyclopedia gets better. If you disagree with a change, raise it on the page's discussion rather than simply changing it back.