Lethal Tempo and Conqueror are the most consistent rune pages for Azir. You typically run these runes against Bruisers, tanks, and short ranged champions and play off of your auto-attacks. Lethal Tempo is the better one of the two. The buff you get from Lethal Tempo is just more valuable than what you get from Conqueror. Conqueror is a good alternate if you feel like you need more sustain more than attack speed.

This rune page is very good into short ranged assassins that can't really reach you like Talon, Akali, and Qiyana. You can bully then out of lane with this rune.

I usually go First Strike if I'm against a full team of squishy champs, or short range tanks that I can't kill. And just stack on First Strike.

Run Arcane Comet against long-ranged matchups and trade pokes. Also good against short-ranged Assassins. Change Cheap Shot for Taste of Blood for sustain. Ingenious Hunter for Ultimate Hunter if you aren't going Luden's Tempest.

Your build path is quite literally the same every single time.

I almost always go with this build every game, unless the enemy team has no tanks at all. Then I would use the other build. The items that you swap for, with the situational items or the other AP items, depends on you. See what items you need, and what items you don't for your current game.

OTHER AP ITEMS:
Lich Bane for more Auto damage | Riftmaker if enemy stacks HP | Rod of Ages for mana | Rylai's Crystal Scepter against high mobility or short range | Stormsurge against teams with no tanks.

SITUATIONAL ITEMS:
Buy Morellonomicon if the enemy has a lot of healing. Banshee's Veil against CC or heavy AP. And Mejai's Soulstealer if you are super fed.