Here's how legacy storm works to anyone unfamiliar with it.
Generally before you decide to start the combo chain, you are going to want to sculpt your hand using Preordain/Ponder/Brainstorm once you have a couple rituals,
Lion's Eye Diamond
and
Infernal Tutor
you're good to go. Worth noting you don't need those cards exactly, but in the majority of games you are going to want most of them. Here's how to execute the combo chain.
1) Make sure the way is clear with Cabal Therapy/Gitaxian Probe/Duress. While this step is optional (especially against opponents you know don't have counters like elves), in most cases it's often best to check if you can
2) Chain rituals together (Dark Ritual/
Cabal Ritual
) to get lots of mana
3) play
Lion's Eye Diamond
and then
Infernal Tutor
. Hold priority and with the tutor on the stack, sac the diamond for. This discards your hand so when the tutor resolves you are helbent
4) grab and cast Past in Flames
5) Remember those used tutors you cast and put in your graveyard? Time to cast them a second time to increase storm count and get more mana.
6) cast the
Infernal Tutor
from your graveyard getting Tendrils of Agony and cast it. If you did everything right you should have a decent storm count by now which copies tendrils and kills your opponent.
If you plan ahead but know you won't have enough storm to kill them with tendrils in one go, you can instead grab Empty the Warrens and kill them over a couple turns. Obviously you would prefer to kill them on the spot but sometimes that isn't an option.