Fusions

 

1. The Namekian Way
The first type seen was the fusion of Piccolo and Nail.
Only Nameks can do this type.
Nothing specific is done, they just stand next to each other and yell.
Piccolo also fused with Kami this way.

2. The Dance
The second type done and seen was the fusion dance.
If performed incorrectly, the people will still be fused, but not properly (something will be abnormal, they might be very fat).
The power levels of the people have to be the same, but that isn't a problem since Saiyans can change their levels.
Both Piccolo and Goku knew the dance, but it was never said where they learned it.
Goku and Piccolo taught Goten and Trunks the dance, and they became Gotenks.
Gotenks isn't controlled by either Goten or Trunks, he is another personality himself.
He has his own voice and attitude, and is quite strong.
This technique only lasts 30 minutes.
The second time this fusion was seen was the fusion of Goku and Vegeta.
They became Gogeta, another very powerful opponent.

3. The Earrings
The third method of fusion was done by Goku and Vegeta.
They each put on an orane yellow earing, and became Vegetto.
This fusion is permanent, but is probably the best method if you want a strong result.
The earings were provided by the old Kaiohshin, who fused with a witch many years ago.