Try to save some cards for later. If you run out of cards, you will have to rely on the 1 card you draw every turn being the card that you need. You will not have any room for error.
Sometimes it is wiser to wait and not play as forcefully at the start of the Duel, just so that you have cards later on. If your opponent has used all of his/her cards and has nothing left, then you will have the card advantage and be in a better position.
For example, if you have "Fissure" in your hand, but you can destroy your opponent's monster with an attack, you might want to attack the monster and destroy it, and save your "Fissure" for later to use on a monster you cannot destroy in battle.