Phantom Assassin is a melee agility hard carry. She has good chasing potential and the ability to deal four figure damage, making her one of the most popular heroes in non-competitive Dota. However, she requires a lot of farm.
Skills
Put your first point into Stifling Dagger. Max it first as well. Use it to secure last hits in the early laning phase or if playing defensively. Later on use it to harass and chase down enemies.
Put your second point into Phantom Strike and max it second. This can be used defensively as well as against opponents.
Max Blur last but get a value point in it at level 4 for its passive effects and evasion chance.
Always get Coup de Grace (levels 6, 11 and 16). Hit enemies and pray it procs!
Items
Starting Items (Safe Farm) - A set of Tangos, a Healing Salve, 3x Iron Branches, and a Quelling Blade.
Starting Items (Contested Lanes) - A set of Tangos, a Healing Salve, 2x Iron Branches, and a Stout Shield.
Core Early - Magic Wand, Poor Man's Shield, Phase Boots or Power Treads.
Core Mid (If Farming Well) - Battle Fury, Helm of the Dominator.
Core Mid (If Farming Poorly) - Drums of Endurance, Vladmir's Offering. Armlet is also a possibility.
Luxury Options - Black King Bar, Abyssal Blade, Satanic, Butterfly, Monkey King Bar, Assault Cuirass.