Xin Zhao Ap is a champ based in Ability Power and attacks speed
The most important thing is his W: Battle Cry Who allows you to recover tons of HP

Nashor's Tooth Has to be your first item. It gives all the thing Xin Ap need: Ability Power, Attack Speed and allows you to start making damage.
Guinsoo's Rageblade It's another item which gives you all the things needed, and one of the best passives. When you have it, dont scape from any 1 vs 1, just keep attacking, and you wont die.
Rabadon's Deathcap For Tons of AP, boosting you W and Tooth's pasive.
Phantom Dancer Gives a lot of Attack speed, and the needed movement speed.
Normally you have won the match at this moment.
Now comes one thing that i have to explain:
Lich Bane and Trinity Force
You will say: They have the same Unique: SpellBlade, and makes this stupid.
There's an unknown thing by most LOL players: If 2 items have the same unique, only the first one in order will be actived. Explained this, i will continue.
Lich Bane Has to be the first item, because we only want it for its passive, who allows us to make tons of damage: E, 2 secs, W, 2 secs, Q, 2 secs (As Q reduces cooldowns, do it all the time)
Trinity Force Just for completing

Flash It's a nice spell for any situation.

Exhaust It's very nice to slow your opponent.

Smite If you play Xin Zhao in 5 vs 5, you will need this.

Cleanse Can be nice if the enemy has much CC

Pros

- Will not lose HP
- If played in 5 vs 5, can solo Dragon, Baron and towers
- It's so easy

Cons

- Useless in Early
- Can't play without items
- Can be destroyed with CC

AP Xin Zhao has two counters:

Teemo If you can't hit, you can't recover HP.

Sion Recovers more HP than Xin