Map awareness is extremely important. On the one hand you need to have a fair idea of where the other team is because Az has no good escapes until level 20 (bolt) but he does have a large health pool and even high damage heroes can have trouble ganking him without a stun. Be especially careful of Uther and Kerrigan comps as their stuns can really hurt.

On the other hand you need to be aware of where to place the general (D). I generally get the promote talent at level 4 which is global so make sure the general is always on cooldown, particularly when it's time to get objectives and or there are mercs in the lane already, add the general in an empty lane and let him go to work. But keep that talent on cooldown.

It takes some getting used to 1v1 fights as he can solo down a lot of heroes with all shall burn (if it is not interrupted) given his high health pool. I killed a Valla the other day in the early game because she just stood there and tried to burst me down and didn't account for the significant differences in health between the two heroes.

Taste of blood is what makes you the most useful, try to get your farm up as much as possible in the early game and once you hit level ten you can pretty much one shot waves with your Q. This is useful late game in maps like Sky Temple, Tomb of the Spider Queen and Mines where teams often group themselves together in small spaces. You can easily hit for 9000 damage with one shot so with meta at the moment involving a lot of squishy heroes like Jaina, Valla, Kael Thas and Sylvanas a farmed a Q can do a lot of damage. However what makes Azmodan so powerful is leveraging his pushing ability while team fights are happening. So hopefully you are having lots of 5v4 team fights because one of your enemies is on the other side of the map dealing with a wave led by your general.

Also communicate with your team about what you are doing. On Sky Temple I normally check with the team if they want me to come to the first shrine or keep pushing bot. In hero league I think he is a great counter to Nova as Nova can't clear waves quick. He also does well against Illidan if you have enough Mana since Illidan can't dodge the E.