GETTING STARTED
If you're a beginner, feel free to come in. Us regulars can get a bit technical with card evaluations and use a lot of jargon, and many of us will loudly proclaim that a cool-looking card is junk, or say that a lame-looking card is really powerful, so ask us if you want an explanation.
To see what a game is like, check out Geek and Sundry's Spellslinger series (now discontinued), where Day[9] battled various geek celebrities, often losing, using simple and easy to follow decks.
To get started, check out the official page. Basically:
* It's recommended that new players play Magic Duels (thread). It's a great way to learn the game on your own, and it's free!
* After that point, the act of deck building can be intimidating, so it's recommended that you try out a preconstructed deck and customize it with other cards you get, before you start making your own from scratch. Planeswalker Decks are preconstructed decks that come with four unique new cards, including a new Planeswalker card. If you have a friend to play with, there are also Duel Decks that provide two decks for a game right out of the box, but are a bit more complicated.
* To get your physical collection started, buy a Deck Builder's Toolkit, which includes not just a starting collection of cards (including a lot of lands), but also some booster packs and a good box to store cards in. The Holiday Gift Box provides an even larger starting collection and better storage.
* The different play formats can be found here. The most popular formats where you start out with no deck and have to make them from scratch (Limited) are Draft and Sealed. The most popular formats where you bring a 60-card deck ahead of time (Constructed) are Standard, Modern, and Legacy. Casual play has no restrictions other than what your friends decide. Once your skill advances, another popular way to play Magic casually is Commander.
* While game stores will often hold Magic events at other times, every store that has Magic events will have Friday Night Magic. There, you will be able to find other players in your area to both have matches with and trade with. Find game stores here. And to get started participating in your local game store (LGS) scene, attend an open house or prerelease event!