Science of the Great Ape
The cycle of the Great Ape is first started by caused by Blutz Waves. All Saiyans are born with a tail, when a full moon arises it sends many Blutz Waves and the Blutz Waves touch the Saiyans tail. When the Blutz Waves touch their tail it transforms them into a Great Ape. It doesn't have to be the moons Blutz Waves, it could be any large amount of Blutz Waves. Like in the Baby Saga, Baby Vegeta forced Bulma to use her Blutz machine to make him go Golden Great Ape. Vegeta seems to be one of the only saiyans who can talk in this form.
The transformation increases the Saiyans power ×10 so great, that Great Ape Vegeta in the Saiyan saga had a power level of 180,000. You have to be trained to be able to control your self in this form. Like Vegeta he was able to control himself in this form.