How to Play Magic: The Basics
The part of your deck that sits facedown on the field, which you draw from every turn to get new cards to play.
Where instants and sorceries go after they are used, and where destroyed creatures, land, enchantments, and artifacts go.
cutting the deck
Picking up a random number of cards off the top of your deck and looking at the card on the bottom of the pile; usually done to see who goes first in a game.
What happens when a player does not have any more cards left to draw from in his/her library. When you deck out, you lose the game automatically.
To play Magic, you need a deck with at least 60 cards in it, and at least one other person to play against. You and your opponent both start out with 20 life points, and your job is to get your opponent down to 0 life points before he or she gets you down to 0. Whoever gets to 0 first loses.
Determining Who Goes First and # of Cards to Draw
In any Magic game, you begin by drawing 7 cards from your library, and choose who should go first by either rolling a die to decide, or by cutting your deck to a random card and letting the person with the higher mana cost go first. The person who goes first does not draw before beginning his/her first turn; the person who goes second does draw. If you're playing multiplayer (more than 2 players), everybody draws before beginning their first turns. If you have a hand that has more than 7 cards at the end of your turn, you must discard cards to the graveyard until you have only 7 again.
Playing Lands for Resources
You can only play one land a turn, but it's usually good to have 2-3 lands in your hand to begin with, as well as cards that you can play easily in the first few turns. A hand with no land, or a hand that has a lot of very high mana costs, means that you'll be at the mercy of the other player for the first few turns, until you can get the land to play what's in your hand. Getting a good defense, a good offense, or a good control base in place in the first 1-2 turns is key!
Which Cards Stay in Play and Which Don't?
Also, look carefully at the types of cards you're playing. Some cards stay out permanently once you play them, like lands, creatures, enchantments, and artifacts--that is, unless your opponent does something to get rid of them! But instants and sorceries go directly into the graveyard after you play them. I usually try to place instants and sorceries directly into the graveyard when I play them, so I don't leave them out on the battlefield and get confused.
Winning the Game: Many Roads to Rome!
As for winning the game, how you choose to get your opponent down to 0 is completely up to you. You can make the person lose life or take damage with direct life-loss and/or damage spells, or you can use creatures to attack the opponent and make them take combat damage. Another type of win condition is decking out the opponent, making them draw a lot of cards. You can also, of course, blend two or more of these strategies to make your own winning style. See more tips on gameplay in my M:TG Gameplay article!