There are 3 kinds of fusion. The first kind is the fusion dance. It is done by performing a silly dance and can last for about 30 minutes depending on the SSJ level (example: If Goku and Vegitta used fusion at SSJ4, the time will be only 10 minutes instead of 30.) The persons must be at the same height and Ki and it can only be done once in 30 minutes.

Characters who performed this:
Goku + Vegitta = Gojeta
Trunks + Goten = Gotenks

The other fusion is the one that has the earrings given by the elder Kaioshin. To perform this, the characters must put both earrings at the opposite ear and they will be magnetized to become a new fighter. The power output is much greater than the fusion dance because its formula is (a + b) x 10 where a and b are the one to be fused with each other. It can only be done by the same person once in a lifetime and is permanent...( At least that what that episode says...)

Characters who preformed this:
Goku + Vegitta = Vegetto
Shin + Kibito = Kaioshin
Unknown witch + Elder = Elder Kaioshin

The third fusion is the absorbtion of the Nameks to one another. They will combine using the host body and their power will be combined. This fusion is permanent even after death.