Because rid, meaning to free from, is uninflected in its past-tense, perfect, and past-participle forms, ridded is a superfluous word. It’s listed in a few dictionaries, but most usage authorities recommend against it. So, for example, “we rid ourselves of it yesterday” and “we have rid ourselves of all our belongings” are correct.
Ridden is a useful word, but it has nothing to do with the verb rid. It’s a participle of ride, and it’s an adjective meaning afflicted or dominated by something.
Ridded appears occasionally—for example:
Among the houses he has ridded of spirits was a former Asian gambling den in North Perth and the Guildford Hotel. [Perth Now]
LaBrie told jurors that she thought her son had been ridded of cancer. [Boston Globe]
After quietly welcoming a U.S. invasion that ridded the country of the Taliban in 2001, it’s now playing a double game. [San Francisco Chronicle]
But ridded, as used in these examples, is much more common:
Mr. Calderàn is now rid of a diplomat whose “ignorance … translates into a distortion of what is happening in Mexico.” [Wall Street Journal]
The Jayhawks believe they rid themselves of a significant upset demon by getting past the round of 32. [ESPN]