The presents are placed in piles in the middle of the players. This determines each persons turn to pick a present. All players take one turn for each number, and all players go in the order of the numbers they have picked. Fore instance, a woman usually takes a woman's present, but it is not necessarily. You pick your present based only on the look, feel, and sound of the package, none of the presents are opened until the game is over.
Every person has to choose between taking a present from the pile or from someone else.
You can take a present from anyone that has a present, but you can not take the last present from someone that has no more numbers. Then the next number goes. And Yes, you may take a present from another group, a woman can take a man's present, for example. The generic presents will fill in the gap. I have seen a young man take a woman's present because he thought his girl friend would like it.