Lina is a fantastic nuker, with extremely high burst magic damage abilities and a decent disable, all of which have low cooldowns. For this reason, and because she is fairly item independent, Lina is most commonly played as a lane support or roaming support.
Skills
Skill Dragon Slave second but max it first for its more reliable AoE damage.
Skill Light Strike Array first and max it second. Remember the stun has a lengthy delay.
Skill and max Fiery Soul last.
Always skill Laguna Blade (levels 6, 11 and 16). Use to soften up an enemy in ganks/teamfights or to secure a kill on an enemy who will almost certainly get away on low life if you don't use it.
Items
Starting Items: A set of Tangos, Healing Salve, Courier and/or Observer Wards, Iron Branches.
Early Game: Flying Courier, Observer Wards, Boots of Speed, Magic Wand, Bracer.
Core Items: Arcane Boots and one of: Blink Dagger, Force Staff, Mekanism.
Luxury Item Possibilities: Drums of Endurance, Eul's Scepter of Divinity, Heaven's Halberd, Scythe of Vyse, Dagon, Ethereal Blade, Veil of Discord, Aghanim's Scepter, Bloodstone, Orchid Malevolence.
Situational Items: Sentry Wards, Smoke of Deceit, Dust of Appearance, Gem of True Sight, Necronomicon.