If a Saiya-Jin possesses a tail, then he or she will transform into a giant monkey form, known as Oozaru. Their strength will triple and this will give them that extra boost that they need to take over a planet. A Saiya-Jin can not control itself during its Oozaru form by nature. This requires strict training and usually starts at a really young age.
The transformation occurs only during a full moon; this sends out moonwaves on a certain wavelength that enables the Saiya-Jin to transform. This can only occur if they still hvae a tail.
If not, their power will still increases greatly, although not nearly as much as when they are in their Oozaru form.
The power of the full moon can be simulated by creating certain types of energy. This invention was done by one of the third class soldiers when he was the last one standing. He created this energy ball, was able to transform, destroyed everything around him, and conquered the entire planet by himself.
The powers of the Oozaru are great. Not only is an Oozaru immensely high (probably 10 meters), he is also immensely strong and fast. He can not create any energy with his hands or the rest of his body as usual. Instead, he gathers power from inside, and is able to shoot energy beams from his mouth.