Searcher

A Searcher is any card, upon meeting of it's effect requirements (assuming the card has any), is capable of letting you pick a monster(s) from your Deck, and either summon it/them to the field, or add it/them to your hand, usually within a restriction placed upon you by the card itself.

Two of the best searchers are Sangan and Witch of the Black Forest, but others include UFO Turtle, Shining Angel, UFOroid, Mystic Tomato, Giant Rat, and Mother Grizzly. Last Will can also technically be considered a Searcher.