It teaches that there is one Torah, which is what Rabbinic Judaism refers to as the Written Torah, and itself refers to simply as the Torah.
It doesn't acknowledge what Rabbinic Judaism refers to as the Oral Torah.
According to the Karaite Korner Web site, "Karaism is the original form of Judaism as prescribed by G-d in the Torah." That is, the Talmud and Midrash are considered commentaries and interpretations of the Torah, but these early interpretations receive no greater weight than current understandings.
The majority of Karaite Jews live in Israel, but some live elsewhere including a few thousand in the U.S.