Runes are similar to other AP mages. AP quins, Armor seals, 3x AP glyphs and 6x scalling CD glyphs and AS marks.
You need AP and this AS is to apply Thunderlord in lane trades.
CD from runes at lvl 18 will be 10 %, from items you get 30% so in total 40 % CD.

Savagery is mainly to help you with farming - + 5 Dmg on your basics. I take cause I do not see sense in taking + 3% MS out of combat.
Secret Stash is useful mastery for laning phase due to improving your HP potions into pies.
I put points into meditation to restore mana (which you lose in early quite quicky) rather then into merciless, but could be a option as well.
Dangerous game is the next mastery you need to put point into. HP and mana resets are quite fine eventhough this mastery is quite bad (better than the other one)
Precision is the perk you want to have. I find 40% CD enough and bonus penetration is very useful.
And finally the Thunderlords Decree, which is the core mastery for azir.
Other points in Ferocity are not as important as those, still useful.

You start with Dorans ring and 2 potions. First item has to be Nashor, after that build Sorc boots and Rylai. When finished buy Zhonya, Rabadon and Void in order you need.

Simply forst max q, than w and last e (maxing e second is not bad, but w is just better)

Play Video Watch this, it is quite old, the knock-up is already gone :(, next the option to cas w on turret is gone too and passive is slightly nerfed (only the turret remains:D)

Great early and late, he falls a bit in mid game.
He is different from other mids, while you have to think about your actions, not just throw spells.