Kunkka may be played solo or with a partner. You want to focus on farming to gain a heavy item advantage over the enemy team. He is considered a hard carry, but is a good ganker. So don't forget to help your teammates with you ganks.
Early on, Kunkka will want to make the most of Tidebringer by playing extremely defensively. The bonus damage and cleave it provides allows you to last-hit creeps and harass your opponent simultaneously, and hence you should try to always angle yourself so that you're able to hit as many heroes as possible. In general, you should stay back until Tidebringer is off cooldown, only attacking to kill a creep and trigger second skill. This will minimize the damage you take.
Once you have a few levels in Torrent, you can try to trap enemies with it. Remember that the cast position of Torrent is invisible to enemies; they have to guess where you put it. If you catch them, you may follow up with a damaging Tidebringer.
In team fights, you should always start out with Torrent then call Ghost Ship before the Torrent triggers. Ghost Ship is extremely difficult to use due to its set range, so try to gauge your opponent closely before using the combo. Follow this up by using your Shadow Blade and run towards the enemy. Try to hit as many enemy heroes as possible with Tidebringer, and remember to activate your Shadow Blade again once the cooldown is gone.
Torrent can be used to harass. Save mana for 1 to escape/initiate.
Ship can wait till 9, you won't need it too much in lane.
X Marks the Spot won't be needed till later with a lower cooldown it's best used to gank or catch fleeing heroes after a team fight.
Shadow Blade dmg bonus is multiplied with Tidebringer plus a crit from Daedalus will hurt a lot.