Planeswalkers are powerful allies you can call on to fight by your side. But how do they work?
Planeswalker cards are shuffled into your deck at the start of the game, just like any other cards. You can play a planeswalker only at the time you could play a sorcery. A planeswalker is a permanent, so when a planeswalker spell you control resolves, it enters the battlefield under your control. (Note that planeswalkers are not creatures.)
Each planeswalker has a subtype. For example, Sarkhan Vol says "Planeswalker — Sarkhan" on his type line. If a player controls two or more planeswalkers that share a subtype, that player chooses one to keep and puts the rest into their owners’ graveyards.
The number in the lower right corner of a planeswalker card is its "loyalty." It enters the battlefield with that many loyalty counters on it. If it's ever on the battlefield with with no loyalty counters on it, it's put into its owner's graveyard.
Each planeswalker has a number of activated abilities on it. You can play one of these abilities only at the time you could play a sorcery, and only if none of that planeswalker's abilities have been played yet that turn.
The cost to play a planeswalker's ability is to add or remove a certain number of loyalty counters from it. For example, the symbol means "Put 1 loyalty counter on this planeswalker," and the symbol means "Remove 3 loyalty counters from this planeswalker." You can't play an ability with a negative loyalty cost unless the planeswalker has at least that many loyalty counters on it.
Fighting a Planeswalker
Planeswalkers can be attacked. When you declare attacking creatures, you choose whether each one is attacking your opponent or a planeswalker that opponent controls. Your opponent can block as normal, regardless of what each creature is attacking. If a creature deals combat damage to a planeswalker, that many loyalty counters are removed from it.
Other sources can deal damage to planeswalkers. If a spell or ability you control would deal damage to an opponent, you may have it deal that damage to a planeswalker that opponent controls instead. So while you can't target a planeswalker with a Shock, you can have a Shock that targets your opponent deal 2 damage to one of his or her planeswalkers instead of to the player. You can't split the damage from one source between a player and a planeswalker. Damage dealt to a planeswalker results in that many loyalty counters being removed from it.