Against azir, Once Azir has picked up his Nashor's Tooth, he is going to push the wave really quickly. Try to keep the wave as even as possible by matching his damage on the minion wave. If he uses an ability, you’ll need to use one too.

The best time to fight Azir is when Soldiers W are down. This is because he will lack a lot of damage. Try to start fights whenever he has no Soldiers W available. 

After Azir hits level 6, he will have a lot more protection and can disengage quite easily thanks to his Ultimate R. While his Ultimate R is down, try to abuse the cooldown and look for kills. Against azir, Once Azir has taken his Nashor Dent, he will push the wave very quickly. Try to keep the wave as well as possible by matching his damage on the minion wave. If he uses a capability, you will need to use one too. The best time to fight Azir is when the W soldiers are down. That's because he will lack a lot of damage. Try to start fighting every time he doesn't have W soldiers available. After Azir touches level 6, he will have much more protection and can easily disengage thanks to his Ultimate R. While his Ultimate R is down, try to abuse cooldown and look for killers.