6 Inferno became largely popularized in patch 9.24B, and has stuck around a solid option when you find many defensive items. 6 Inferno will do immense damage over team, so finding lots of defensive items will ensure your team stays alive long enough for the enemy to burn.
When you find a lot of defensive items, or are able to find early Inferno units such as Kindred or Zyra.
In the early game, Nasus or any warden really will be a huge help to hold your defensive items that will later go on Amumu. Try to get 3 inferno as soon as possible and start win streaking.
By the mid game you definitely want to have your Kindred + Varus combo up as this will help the most in win streaking through the mid game. Continue to use a warden front line and start putting in your best units while you slowly level up to 7 and 8.
Since this comp relies on win streaking, it is okay to make good general items early on like Guardian Angel, Morellonomicon, or Locket of the Iron Solari. All of these items are powerful late game and can be used in other comps even if you can't find your inferno units.
Amumu is definitely one of the main carries of this build, so while win streaking is a priority, don't ruin your economy by doing so. Reaching level 8 and hitting those legendary units will push you into top 3 or top 2.
In the mid game, be flexible with what units you find like shadow or 4 rangers to help ease the transition into 6 inferno. Don't over commit on units you won't be keeping as it will ruin your economy.