The Valar don't really appear in The Lord of the Rings, but they are in The Silmarillion. The Valar are: Manwe (king of the Valar), Ulmo, Aule, Orome, Mandos, Lorien, Tulkas, Varda, Yavanna, Nienna, Este, Vaire, Vana and Nessa.

Melkor, Sauron's master, is a banished Vala.

As the Silmarillion is extremely difficult to summarize with any brevity, I will answer your questions about Melkor, Sauron, etc. only. The Ainur were created by Eru Illuvatar, the All Father, in the beginning. Now, the Ainur made a music according to the great theme of Illuvatar, and for a time, it was perfect and beautiful. However, Melkor, one of the greatest of the Ainur, grew proud, and brought a note of discord into the Music, and the two themes warred with each other before Illuvatar caused the Music to end with one final, resounding chord. Case in point, out of the Music, including the discord of Melkor, Eru Illuvatar created Ea, that is, the Universe. Fourteen of the Ainur grew enamored of the beauty of Arda; one, Melkor, saw the chance for power in it. These along with an unknown number of Maiar (Ainur of less power and stature than the others) entered into Arda, or earth. On Arda, the Ainur who entered it were known as the Valar. Melkor, however, was not counted among them. There were seven "Lords of the Valar": Manwe, Ulmo, Aule, Namo Mandos, Orome, Irmo Lorien, and Tulkas. There were seven Valier "Queens of the Valar:" Varda, Yavanna, Nienna, Vaire, Este, Vana, and Nessa. Valar and their spouses Manwe-Varda Ulmo-none Aule-Yavanna Namo Mandos-Vaire Nienna-none Irmo Lorien-Este Orome-Vana Tulkas-Nessa Sauron's Relationship to Melkor Sauron was originally a Maiar of Aule, that is, he was skilled in the making and ordering of things. He "defected" to Melkor, and became his greatest servant. Other Maiar that served Melkor were the Balrogs, Maiar who had assumed the form of fiery demons. It is to be supposed that they served Melkor from the beginning.