Anti-Mage is a highly mobile hard carry. His low cooldown Blink gives him excellent chasing potential and provides him with a crucial escape mechanism, whilst his passive Mana Break makes him a particularly obnoxious carry for magic-damage dealers, supports, and carries that rely on a healthy mana pool.
Skills
Typically max Mana Break first.
Skill Blink first in case you need to escape from an early gank, max it second.
Max Spell Shield last, though get an early point in it if against an aggressive magic damage line-up.
Always skill your ultimate, Mana Void (levels 6, 11 and 16).
Items
Starting Items: Tangos, Healing Salve, Stout Shield, 2x Iron Branches.
Early Game: Power Treads, Ring of Health.
Core Item: Battle Fury (for farming, not fighting! Go flash farm the jungle).
Luxury Items: Manta Style, Heart of Tarrasque, Butterfly, Black King Bar, Abyssal Blade.
Situational Items: Poor Man's Shield, Drums of Endurance, Vladmir's Offering, Monkey King Bar, Boots of Travel.