When you enter the raid, kill a bunch of adds to activate the gate to enter the Black Garden and then run to the first encounter (looks like the arena of the final fight in the original D1 campaign). The first encounter wants you to open four doors while preventing the boss’ insta-wipe mechanic from going off. It introduces three elements used throughout the raid -- Voltaic Charge, Angelics and Shielding, and Tethering.
In the middle of the arena will be the boss molesting a Minotaur. Killing the Minotaur starts the encounter, but also makes the fight harder (you can use a finisher on the Minotaur, which, while funny, is also not recommended). On the right side of the arena is a Vex door shield. There will also be a floating cube in one of three positions and a cross-like object close to the door. If you shoot the cube it opens up and will tether someone close to it within line-of-sight. That person can then tether someone close to them, and so on. The tether is normally white, but will turn red-ish-orange if you near its limit. While you're tethered you cannot shoot or use abilities (not important now, but will matter in later encounters). The goal is to use the tether to connect the cube to the cross. The first one can be done with three people, but four makes it easy.
Once the door goes down, that starts the encounter. Break up into two teams of three. Team 1 will go through the door and see the next door that needs to be opened while Team 2 will stay with the boss. Team 1 will have a bunch of adds, a Cyclops (possibly two, I can't remember..), and a named Quantum Minotaur. I believe the Minotaur is just there to mess with you, but I can't remember for sure. The initial goal is to kill the Cyclops which will send two Cyclopes back to Team 2 in the initial area. Be sure to announce when the Cyclops dies as having one spawn on you unexpectedly can lead to expected badness. After Team 2 kills their Cyclopes, a named Hydra enemy, the Angelic, will spawn. Kill this quickly and then look around for another one of those cubes. Like in the initial area, the goal here is to tether from the cube to the cross to open the door.
For Team 2, adds will spawn in two sets. There will be an initial wave of adds and then a wave with Minotaurs. When the Minotaurs spawn, the boss will also start to move. It'll randomly go somewhere in the room and shoot out a white cube-ish-looking thing of energy (I believe it also does one like 30 seconds after the encounter starts, so be aware of that as well). If you leave this sitting there, it'll wipe the encounter. One person needs to run into the energy which will pick it up and give that person a debuff called Voltaic Overflow. This debuff is on a timer and if you pick up another charge, it'll kill you. There's nothing that happens if the timer reaches zero, it is just there to prevent you from picking up another charge too quickly. Also, multiple people can get the debuff if you run through it at the same time, so make sure you have an order in place beforehand. Essentially you have to get everything I've talked about to this point done in three energy drops.
After the Team 1 opens the second door, the boss will leave the initial area and go down to the second door. At this point, Team 2 needs to leapfrog Team 1 and the two groups will switch roles -- Team 2 has to kill a Cyclops, deal with the Minotaur, kill the Angelic, and connect the cube while Team 1 is now in charge of collecting Voltaic Overflow and dealing with the two Cyclopes that spawn. After the third door opens, the boss leaves again and Team 1 leapfrogs Team 2 and moves to the next area. Repeat the process again, but in this area, there will be three locks on the door. Unlock the first lock and the boss will leave (when you are facing the door, I believe it is the one to the right). At this point, Team 2 needs to come up to join Team 1 and you can unlock the last two locks.
When you unlock the fourth door, run into the next area and you'll see a field of Cyclopes. The boss will put down three or four energies and you will need to run and collect them while dodging/killing the Cyclopes. When you collect the last energy, the encounter ends and you get your loot.
After this there is a jumping puzzle to the next encounter where you can find a secret chest. When you fall down a hole, go to the left side, and near a platform going up and down, there will be a small hidden room.