Here are the ways the characters from dbz/gt fuse into one
1.Fusion Dance- This is the most common way of fusion i'd say. Two people do a weird dance which their index fingers must touch. The people that do use this are about the same age. Like Goku and Vegeta and Goten and Trunks. This only lasts for about 30 mins.
2.Potara Earings- This is a way two people can stay fused for as long as they want. Goku receives these form Kaioshin. When doing the fusion dance one person has one earing on and the other person has the other earing on.
Some fusions are:
Goku+Vegeta=Gogeta
Potara earings+Goku+Vegeta=Veggito
Chibi Trunks+Goten=Gotenks
(According to Goku)Piccolo+Kami=Kamiccolo