A common variation is to play cutthroat, where such passing of cards does not take place. The deck consists of twelve cards in each of four suits - two in each of the ranks Ace, Ten, King, Queen, Jack, and Nine. For the first round of a game, the players select a dealer in whatever manner they choose. At our house, it's generally whoever happens to pick up the cards first. The dealer shuffles the cards in whatever manner is convenient to mix them thoroughly.
Some players insist that the cards be dealt one at a time.
I was taught to deal the cards three at a time, and continue to do so. All 48 cards will have been dealt. It is generally courteous to wait until all the cards have been dealt before picking up your hand. Once the cards have been dealt, the players pick up, sort, and examine their hands. The next phase is bidding.