The base rules of Magic: The Gathering are no more complex than any other card game, such as Poker or Bridge.
You start the game with 20 life pointns and a deck of 60 cards, unless you're playing the Commander variant, in which case you start with 40 life and 100 cards.
At the start of the game, you draw 7 cards into your hand.
On your turn, you:
In combat, you tap any number of your creatures. Creatures attack your opponent, never a specific card, but your opponent may choose to intercept or block your creatures with creatures of their own.
Tapped creatures cannot block.
Each creature has a Power and Toughness value, indicated in the bottom right corner of each creature card. When one creature's Power is equal to or greater than another's Toughness, it destroys that card, sending it to its player's discard pile (or graveyard). Damage during combat happens simultaneously, so it's entirely possible for two creatures to destroy each other during combat.
A creature can be blocked by more than one creature, too. Your opponent gets to decide the order of blocking, so resolve damage on the first card, and then on the second card, and so on.
When your opponent has no way to block, or chooses not to block, then the damage (the value of your creature's Power) is deducted from the player's life total.
Those are the rules of Magic: The Gathering, defined by sections 1 to 5 of the official rules document on wizards.com.
However, the base rules are only the foundation. In fact, sections 1 through 5 of the official rules make up only one third of the rules document. That's because by design, most Magic: The Gathering cards systematically modify the rules of the game.
Additionally, Magic: The Gathering generally encourages its players to build their own decks, which itself is an acquired skill.
When explaining Magic: The Gathering, I like to treat the game itself as a framework, because ultimately it's the player, through building a deck, who defines how each game actually plays. It's impossible to discuss every card in Magic's history (there are well over 25,000 unique cards), and every new set contains, on average, two new mechanics.
What is possible, though, is to discuss the functions that different types of cards serve. By understanding the mechanical roles that any given Magic card may encompass, you learn what kinds of cards to look for when you purchase or trade them so you can build decks that make for an enjoyable game.
Before discussing card roles, though, it's important to consider a target budget. Magic designers use card rarity as a way to limit the potential power level of a Magic: The Gathering game. Cards with almost game-breaking abilities aren't printed in great number, so the demand and prices go up, and so they're not often seen in actual gameplay. Historically, however, once a rare and powerful card has become popular, the designers tend to borrow ideas from it, distributing the strategy that it represents among common and affordable cards.
In all of my categories for card roles, there are quintessential examples of the strategy. Those are usually the rare cards that set the precedence for the card role in the first place, and so they are almost always prohibitively expensive. For that reason, the example cards I cite are meant to illustrate a spectrum of cards that work toward, if not exemplify, the card role I've identified. I rarely bother listing the "obvious" card for a role, and instead limit my card lists to inexpensive ($2 and under) cards.
In all cases, my card list is incomplete and purely demonstrative. The best way for you to find cards, whether I've listed it or not, to fill a card role is usually an Internet search. Not just a few sites that track Magic: The Gathering cards offer lists of cards that fit a specific strategical need, or that can serve as a weaker and cheaper replacement for a popular rare card, and so on. Build a deck on paper first, and then purchase the single cards you need from your local game store or a reliable Internet game site.
Whether they take the form of a summoned Creature, an Enchantment boosting other cards, a Sorcery or Instant or Artifact, the bulk of cards in Magic: The Gathering perpetuate or mitigate inevitable combat.
General purpose cards cost a full spectrum of mana amounts and color. Some, you can play for 1 or 2 mana, while others require 4 and 5 and more. Some require just one color of mana, while others require a mix of colors, and others (mostly Artifacts) don't care about color at all. Many have special abilities, and may possess synergy with other cards. Strategically, though, these cards are mainly meant as "cannon fodder". They're the cards that get placed on the battlefield as a display of either offensive or defensive force. They're the weapons you use to intimidate and then destroy your opponent.
Combat cards are a necessity of the game because the main avenue to victory is direct combat. Whether or not that's the path you take, you'll probably be subject to it. At the very least, you must be able to defend yourself. Thanks to the way combat is designed, a player with enough 1/1 Creature cards can defend against, and even defeat, a player with big 5/5 and 7/7 Creatures, but be defeated by a player with Flying Creatures, who might themselves be defeated by a player armed with defensive Walls and an arsenal of spells dealing direct player damage.
In other words, Magic: The Gathering has enough variation in combat tactics that the cards you throw into battle are arguably less important than the strategy you develop with other card roles.
The base rules of Magic: The Gathering state that you can only attack your opponent. This means that you normally don't have the option to eliminate an enemy card that's causing you trouble in the game. Some cards, however, enable "card removal" by breaking the base rule and targeting a specific card.
There's usually a strict limit to what you can target.
As you can see, the means of removal may vary. What kind of card is considered a "removal" card depends in part on the situation. For instance, I wouldn't normally Flatten a removal card, but against a 4/4 creature that's exactly what it does.
The base rules of Magic: The Gathering forbid you from attacking your opponent directly, but some cards cause life loss to a player. This is special noncombat damage (which may matter when you're up against a deck with abilities that trigger on combat damage).
Should you reach 0 life points in Magic: The Gathering, you lose the game. Some cards grant you additional life points.
The default source of mana is a Land card. These provide you with mana so you can play cards ("cast spells"). For a 60 card deck, anticipate requiring about 24, using a mix of colored and colorless mana.
The base rules prohibit you from playing more than 1 Land card on each turn. As a result, normally you can never have a mana base greater than the current number of turns you have had. In other words, assuming the best possible hand, you'll have 3 Lands that can produce 3 mana each turn by turn 3, and by turn 7 you'll have 7 Lands that can produce 7 mana each turn, and so on.
However, there are ways to acquire mana aside from Land cards. This is colloquially known as "mana ramp".
By playing both a Land as well as a non-Land card that provides mana, you gain more mana in one turn than is possible when relying on just Land for mana.
These cards tend to be Uncommon or rarer, and prices vary.
Some cards generate tokens that can be converted into mana later. You have to wait for your extra mana to build up into something substantial, and once you spend it, you must start the process over, but it's a good way to increase your mana budget so you have it when you need it.
Some cards provide a discount on mana costs.
Special Land cards can be tapped for one of two or more colors. This doesn't increase your mana, because the Land still only renders 1 mana. However, they can prevent you from coming up short on a specific color of mana in a multi-color deck.
Some cards allow you to untap a tapped Land. As a result, you can tap the Land again during the same turn, producing two mana from one Land.
Some cards allow you to search through your draw deck (your library) for Land. There are details that make some more optimal than others, but all result in a guaranteed Land card either in your hand or on the battlefield. Given that normally you're at the mercy of the randomness of your library, this can help you build a good mana base in a reliable and predictable way.
Because you're often playing two or three cards on your turn, but you're permitted by the rules to draw only one each turn, there's a good chance that you will deplete your hand before the game is over. Some cards give you permission to draw more than just the initial draw-for-turn.
The opposite of granting card draw is called, in Magic terminology, milling. When you Mill a player, you cause them to discard, either out of their hand or from the top of their library.
By default, a card that's discarded (sent to the graveyard) is functionally out of the game. After all, that's the point of a discard pile. However, there are cards that allow you to bring cards back from the graveyard. This is often called recursion by Magic players.
There are opposite effects, too.
Some cards help you "control" the state of the game beyond its normal flow. This is as broad a category as general purpose combat, and could arguably include other strategies, particularly Milling and Recursion. But this category's diversity is why it deserves its own definition. There are many aspects of control, ranging from literally seizing control of an opponent's card, to preventing damage, forcefully tapping cards, and more.
The categories I define are just one interpretation of the game of Magic. They are:
Aside from "combat cards", the names of the categories I identify are widely used terms within the Magic community. The most efficient way to acquire cards within each category is to search the Internet for cards that fall within those categories, and then buy the ones that appeal to you as single cards from your game store.
There are other card categories. For instance, there are powerups (cards that place +1/+1 counters on others, for example), cards that force other cards to tap out of turn, cards to seize control of other Creatures, and so on. These, in my opinion, are avenues toward essentially the same goal: winning. The categories I define don't concern winning as much as they sustain the game you create by building a deck.
Look through Magic: The Gathering cards with these categories in mind, and you'll start to recognize them as variations of the core components of Magic, and you'll be able to make wise decisions on what cards to purchase for your next deck.