It all starts with COUNTING. Let children count all kinds of stuff they see during their play. Use simple counting games, such as:
Have a deck of regular playing cards minus the picture cards. Each person draws a card. The one with a higher number wins all the cards played in that round. This can teach both number recognition and counting, because the child can count those little pictures (hearts, spades, clubs, or diamonds) on the card.
A variation of the one above: deal two cards to each person. The person with a higher TOTAL wins all the cards played in that round. Children will learn basic addition!
Use any board game. Have the markers advance as many steps as a die or dice show. The child will need to count the dots on the die or dice, and then count steps to move his marker.
Lay a bunch of dominoes face down on the table. A child picks one, you pick one. The person with a higher "dot-count" gets both dominoes.
Lay a bunch of dominoes face UP on the table. A child picks one and places it on the table to start the "train". The next person picks one so that its end matches one end of a domino already laid.
Play with marbles or blocks or similar objects. You take some objects, and ask the child to take for himself as many as you have AND ONE more. Then it's the child's turn to take some, and you need to take the same amount plus one more. Reverse the game later to do ONE LESS.