Kunkka is a melee strength hero that is usually played as a mid-lane core or a farming carry.
He is popular largely thanks to his passive cleave ability, Tidebringer, which allows him to deal tremendous damage to the entire enemy team within a 600 range AoE, provided he has enough items.
Skills
Max Tidebringer first for the bonus damage it provides. This allows you to dish out significant harass whilst last-hitting.
Max Torrent second - your main stun, it also does nice magic damage and slows, but can be hard to hit.
Get X Marks the Spot Last. 2 points is sufficient as you can cast it before Torrent to guarantee the latter always hits the enemy. Once you have 2 points in it then max Stats.
Always get Ghost Ship (levels 6, 11 and 16), and cast it in every teamfight. Even if you miss, the bonus rum buff will help your team immensely.
Items
Starting Items: 2x Healing Salve, Circlet, Gauntlets of Strength, Iron Branch OR Healing Salve, Tangos, Gauntlet of Strength, 3x Iron Branch.
Early Core: Phase Boots, Magic Wand, Bracer.
Mid-Game Core: Shadow Blade, Daedalus.
Luxury Extensions: Black King Bar, Assault Cuirass, Daedalus (yes, another one), Battlefury, Monkey King Bar, Heart of Tarrasque.
Situational: Drums of Endurance (if poor or early fighting), Bottle (if mid), Divine Rapier (last-chance late game).