There are 7 total Saiyan transformations that occur in the whole DragonBall series. Here are the details in order from weakest to strongest:
Super Saiyan: For a Saiyan to reach the first transformation of a Super Saiyan, he must have an initiative to go beyond the normal state. When a Saiyan becomes a Super Saiyan; his muscles increase to a small extent, a golden glow occurs around him, and his hair becomes golden blonde. You become much stronger and faster when you are Super Saiyan. Every Saiyan except for pan, can reach this transformation.
Ultra Super Saiyan: This transformation is not necessary in the process between Super Saiyan 1 and 2. Ultra Super Saiyan is commonly accomphlished when the Saiyan uses all his power to try and become Super Saiyan 2. When a Saiyan becomes an Ultra Super Saiyan, his muscles grows, an even bigger golden glow occurs, and his hair becomes erect and more depth is visible in it. Similar to the Ultra Super Saiyan transformation not mentioned. Ultra Super Saiyan increases your strength by very much, but it slows you down very much as well. Brolli, Goku, Mirai Trunks, and Vegeta achieve Ultra Super Saiyan. Gohan was the only Saiyan that achieved Super Saiyan 2 without reaching Ultimate SS.
Super Saiyan 2: This transformation is only triggered by anger. Only a small amount of Saiyan reach Super Saiyan 2 status. When a Saiyan reaches Super Saiyan 2, his body develops more muscle, his body glows luminously, he is surrounded by electricity, and his hair's depth is visible very much. When some Saiyan's are in the Super Saiyan 2 state, they have one strand of hair hanging down on their forehead. Super Saiyan 2 has the same effects of Super Saiyan, except that it is to a greater extent. Only Gogeta, Gohan, Goku, and Vegeta reach Super Saiyan 2.
Oozaru: When exposed to the light of a full moon, a Saiyan involuntarily transforms into a giant ape-like beast. While in this form the Saiyan's power is greatly increased. There are two ways to reverse it, one is to chop off the tail of the Saiyan, and the other is to get rid of the source of moonlight.
Super Saiyan 3: This transformation is the oddest of all the Dragon Ball Z transformations. Much, much training is needed to achieve Super Saiyan 3. Only the elite Saiyan's have the ability to reach Super Saiyan 3. When a Saiyan becomes Super Saiyan 3, their muscles increase slightly, their hair grows down to their knees, and their eyebrows disappear. Super Saiyan 3 wears down a Saiyan's body very much, so this transformation can only be used for a short time. Goku is the only true Saiyan that reaches Super Saiyan 3. However, when Goten and Trunks fuse to becomes Gotenks, the hybrid Gotenks has the ability to reach Super Saiyan 3.
Golden Oozaru: A level that was achieved by Goku and Bebi-Vegeta in Dragon Ball GT. This is the most powerful form of Oozaru, actually, the most powerful of all stages that a Saiyan can achieve, demonstrated by Goku in DBGT episodes 38-40, when he swatted Bedi-Vegeta all over Planet Plant (Bedi's recreation of the Tsufuru home planet.) The main physical difference with the Ougon stage, is that the fur is yellow instead of brown. Also before Planet Vegeta was taken over by the Saiyan, it was also called "Planet Plant", of coarse before renamed to Planet Vegeta.
Super Saiyan 4: The final transformation that a Saiyan is able to achieve. This transformation isn't even considered real by some, because it is only done in Dragon Ball GT, which was not drawn by Akira Toriyama. The first part of this transformation involves a Saiyan having a tail. When a very strong Saiyan looks at the full moon, they become a Golden Oozaru. Similar to the Oozaru transformation, but the fur is gold. Then the Saiyan must be enraged and put all of his anger into himself to reach Super Saiyan 4. If he succeeds, the Golden Oozaru becomes a Super Saiyan 4. Super Saiyan 4 is the strongest transformation, and has no downsides. Once again, Goku is the only Saiyan to become Super Saiyan 4 by himself. Vegeta becomes Super Saiyan 4 because his wife Bulma creates a device called a Brute Wave which stimulates his body turning him into a Super Saiyan 4. And one other Saiyan can reach Super Saiyan 4. The fusion of Super Saiyan 4 Goku and Super Saiyan 4 Vegeta creates Super Saiyan 4 Gogeta, the strongest person in the entire anime.