SAIYANS..........

Saiyans are from the planet Vegeta (what used to be planet Plant). The planet is named after the king of Saiyans, Vegeta. He later gets a son and also calls him Vegeta, this is the Vegeta we know.
Planet Vegeta was destroyed by Frieza. Most of the Saiyans died here. Frieza had already killed king Vegeta.
The surviving Saiyans after planet Vegeta's destruction are: Vegeta, Nappa, Radditz and later in a movie Brolly and his father.
The Saiyans are ruthless and not very advanced. They eliminated a race called the Tuffels which they first shared the planet with, they built a space ship and flew to other planets, took them over, and sold them for money and technology. They were like planet stock brokers. With their ability to become Oozaru's with a full moon they increased in power over 10 times what gave them the advantage to take over. More stages of a saiyan are written below, from weak to strong.

Normal Saiyan:

Normal Saiyans always have black hair, except for half breeds. Like Trunks, he has purple hair but he still is partly Saiyan. Saiyans also have black eyes and a tail, except when it has been removed just like Goku.