From the Wikipedia page , where there is a list of current schools and links to the several websites.
"Schools of Japanese tea ceremony" refers to the various lines or "streams" of the Japanese Way of Tea. The word "schools" here is an English rendering of the Japanese term ryūha (流派).
There are three historical households (家) directly descended from the 16th-century tea master Sen no Rikyū which are dedicated to transmitting the Way of Tea that was developed by their mutual family founder, Sen no Rikyū. They are known collectively as the san-Senke (三千家), or "three Sen houses/families." These are the Omotesenke, Urasenke, and Mushakōjisenke. Another line, which was located in Sakai and therefore called the Sakaisenke (堺千家), was the original Senke (Sen house). Rikyū's natural son, Sen Dōan, took over as head of the Sakaisenke after his father's death, but the Sakaisenke soon disappeared because Dōan had no offspring or successor. The school named Edosenke (江戸千家; lit., Edo Sen house/family) is not descended by blood from the Sen family; its founder, Kawakami Fuhaku (1716–1807), became a tea master under the 7th generation head of the Omotesenke line, and eventually set up a tea house in Edo (Tokyo), where he devoted himself to developing the Omotesenke style of the Way of Tea in Edo.
The san-Senke arose from the fact that three of the four sons of Genpaku Sōtan (Sen no Rikyū's grandson) inherited or built a tea house, and assumed the duty of passing forward the tea ideals and tea methodology of their great-grandfather, Sen no Rikyū. Kōshin Sōsa inherited Fushin-an (不審菴) and became the head (iemoto) of the Omotesenke line; Sensō Sōshitsu inherited Konnichi-an (今日庵) and became iemoto of the Urasenke line; and Ichiō Soshu built Kankyū-an (官休庵) and became iemoto of the Mushakōjisenke line. The names of these three family lines came about from the locations of their estates, as symbolized by their tea houses: the family in the front (omote), the family in the rear (ura), and the family on Mushakōji Street.
The Way of Tea perfected by Sen no Rikyū and furthered by Sen Sōtan is known as wabi-cha. The san-Senke have historically championed this manner of tea.