Fusions
The Fusion Dance
The fusion dance can be done if there is two fighters willing to perform a dance, each doing the same thing, but mirrored. The fusion lasts approximately 30 minutes, then you must defuse and wait 1 hour before fusing once again. The characters have to be around the same length, width, power level, etc. There were four fighters in Dragonball series who did this dance, who were Goku, Vegeta, Trunks, and Goten. Goten & Trunks fuse to become Gotenks, and Goku and Vegeta fuse to form Gogeta. How was this fusion discovered? When Gohan was in OSHS (Orange Star High School-First Year), or during the Great Saiyaman Saga, Goku learned the dance while he was up in heaven. The fusion dance is very cool.
Namekian Fusions
Namekian fusions are probably the easiest to perform, but only Nameks can do this, for example, Piccolo and Nail. They can defuse though. When Piccolo and Kami alse fuse, they can not defuse. It mainly depends on what character you do pick. To perform this fusion, one namekian has to place his hand on the other namek, and that's it! A flash of light and two namekians form into one.
Potara Fusion
So, you want to know how Goku and Vegeta fused into Vegetto? Well, first you have to obtain two rare earrings called Potara Earrings, which was first used by the kaioshins. Each fighter wears an earring on the opposite ear of each other. The permanent fusion can now take place! If you noticed that Goku & Vegeta had defused, that was because of an unexpected condition. Gohan and Goku were originally going to fuse, but Gohan got absorbed by Majin Buu. Vegeta nor Goku can repeat this fusion again, it only allows you to use the earrings once in an entire lifetime.