Their are three types of fusion in the story of Dragon Ball, they are the Fusion Dance, Namekian Fusion, and the Pottera Earing Fusion. All are very effictive, and are used often, the one who is the base of the fusion has control-

Fusion Dance

This type of Fusion is mainly used by Saiyans and only lasts 1/2 hour. Its like the name says a dance. Goku learned this attack in the afterlife during the time of after the infamous Cell Game to when Gohan first enters High School in Satan City. The two warriors who are fusing must be around the same height, weight, and power level, are heros can lower and higher their power levels so power doesnt really matter. This is very hard to do, because the slightest mistake will cause a difective fusion (ex. Goku & Vegeta mess up and become very fat and must unfuse).

Who: Goku & Vegeta= Gogeta (Goku is the Base)
Goten & Trunks= Gotenks (Goten is the Base)
Goku & Vegeta= Veku (Fat Gogeta, Vegeta is the Base)

Namekian Fusion

This Fusion can only used by Nameks and lasts as long as the two warriors who fused want it to. No special earings, dances clothes, or stupid objects are needed to perform this only the Namek who wants to be the base of the fusion, lets the other Namek put his hand on his chest and "puff" the two Nameks fuse. And unlike the dance fusion power, height, and weight do not matter.

Who: Piccolo & Nail= Piccolo (Looks exactly like Picccolo, Piccolo is the base)
Piccolo & Kami= Kamicillo is what Goku calls him at first but Piccolo is the base and claims I am most of this fusion so just call me Piccolo

Pottera Earing Fusion

This fusion is mainly used by Kaioshins but is also used by Vegeta & Goku and the fusion lasts forever, unless something unusual happens. Goku recieves these earings from Rou Kaioshin after Kaioshin & Kibit fuse with them for a demonstration, and is tolled to use them with Gohan. Goku instead has to use them with Vegeta because Gohan was absorbed by Buu. Each person who wants to fuse must wear one earing on the oppisite ear of the other and they hold hands to fuse. This fusion is different in the fact that the two people who fuse voices, clothes, and looks combine.

Who:Vegeta & Goku (Vegeta is the base, they accidently unfuse when they are absorbed by Buu)
Rou Kaioshin & Old Witch (Rou Kaioshin is the base, he tells Goku that an old witch and him accidently fused with the earings and can never unfuse.