Karaite Judaism does not believe the Oral Torah is divinely given, and uses only the Written Torah as the source for their laws. They take the plain meaning of the text and use that as the basis. There's a good article on Wikipedia about Karaites.
The Karaites lived several centuries ago (I think something like 500 remain today). They were very strict fundamentalists who believed that the only 'rulebook; was the Torah and only the Torah in all it's literal meaning. What you call rabbinic Judaism is actual Judaism, and it considers the Talmud (also known as the 'Oral Torah' to be as validly a divine revelation as the Written Torah - the first five books of the Hebrew scripture.
As for the specifics of their daily practices, you'll have to look that up. I doubt they are the same today as they were 500 years ago.
It's like protestants and catholics. Both are wrong in their initial statement (there is a magical dude in the sky) and both went apart from each other by cherry picking what they wanted to believe in ...