Your goal is to stack all of the cards in play into the "foundation piles" in the upper right hand corner of the screen. Cards must be played to these foundation cards in order, starting with Ace, then 2, then 3, and so on through King.
In order to do that you'll need to stack your cards at the bottom of the table in columns of cards in decreasing order. Any card may be stacked on top of another card with a rank 1 higher of the opposite color. So a 5 of Clubs can be stacked on a 6 of Hearts or Diamonds, but not any other rank, and not the 6 of Spades. Once you've started stacking cards, you can move your stacks provided you have enough free slots on the top left hand of the screen. You can always move 1 card for free, but you need 1 slot open in order to move 2 cards, 2 slots open in order to move 3 cards, and so on. If you clear a column of cards on the board, you can also move cards to the open FreeCell spaces there, and can keep as many cards there as you like.
This can be a really tough game to get the hang of! Try to focus on "freeing" the Aces of each suit so that you can start playing cards up to the foundation spaces. Good luck!