During your Draw Phase after you draw a card it is added to your hand. The hand size limit is six, so during your End Phase if you have more than six cards in your hand, you must discard cards until you have six cards left. "Hieroglyph Lithograph" extends the hand limit to seven cards, while "Infinite Cards" removes this limit for both players. There is also no minimum hand size limit, and a hand of zero is still considered a hand.
Certain cards can interact with cards in either yours, your opponent's, or both sets of hands. For example, "Spirit Reaper" can discard 1 card from your hand as part of its effect, and "Exchange" allows you to swap one card from your hand with one card in your opponent's hand. Some cards such as "Raigeki Break" require you to have at least one card in your hand to pay the cost of activation.