Sum Sins has been a staple comp of set 2 almost never completely dying out. There are so many variations to the comp, as many different combinations and itemizations are possible. As such, players can have a hard time mastering the ins and outs of this build, but it can pay off very well once you do.
This comp can work with almost any early game, as it revolves around powerful 3 and 4 cost units. If you are able to find Azir or Qiyana early and upgraded, you can transition into the late game easily with them as your carry.
Since you can use anything early, woodlands are a great choice, and Renekton allows you to add Desert with Azir, and Leblanc lets you transition into assassins earlier.
In the midgame, you should hopefully be able to find Azir and Qiyana as they are what drives your midgame power. During this time, look for powerful summoner units in Yorick and Annie, while trying your best to maintain your economy. At this point, look to have either 3 assassins in or 3 summoners in. Any 3rd assassin will do until you find Zed.
Since Qiyana is one of the core units of the build, use her element while you are transitioning to make full use of her. Examples would be Inferno with Diana or Ocean with Thresh, etc.
In the late game, itemization can be tricky as the items you find will determine what unit you decide to make your carry. If you have electric units, you can make Zed your carry with Guardian Angel Redemption. Or if you have Seraph's, you can make Kha'Zix your carry.
Azir with two items will be a great mid game carry if you can find him early enough.
Guardian Angel is one of the best early items to build for any comp, and stays true for this comp. You can use GA to winstreak and it will still be relavant on Yorick or Zed late game.