Riven's heart chooses one guardian that can carry it at a time. The chosen guardian's name can be seen in the killfeed, and they will have the "Fate's Chosen" buff on the left of their screen. This guardian can pick up the heart and carry it for 15 seconds, after which time they will be teleported inside the heart and seperated from the running team. While the runner is holding the heart, the other guardians must protect them (the runner has no ability to attack or do anything other than run and single jump) and the team should stay relatively close to the runner because the bubble around the runner resets the "Creeping Darkness" debuff. If you are outside of the runner's bubble for too long and the "Creeping Darkness" debuff hits 10, you die and your ghost/revive ends up inside the heart so even if you are revived you can't be the runner at all, drastically reducing the team's overall running time. (Any death will put you inside the heart early, so try not to die at all).
Those not holding the heart should generally move forward of the person with the heart to clear out adds ahead of the runner. Wardcliff coil is fantastic for add clear here if you're sure you won't blow yourself up with it.
When the guardian holding the heart is teleported at the end of the timer, the heart will drop to the ground and another guardian will be chosen, they must pick up the heart ASAP and a new 15 second timer will start. If you are too close to the runner when they teleport out, you might be teleported with them, so keep some distance from the runner when their timer is about to expire (the bubble around them will shrink drastically as time runs out). You can also be teleported inside if you get too close to the heart on the ground after the runner is teleported. Don't approach the heart until a new guardian is chosen (seen in the killfeed) to avoid early teleports, but once you are chosen you have to be really fast to pick up the heart so nobody's Creeping Darkness debuff gets too high.
The timer for Fate's Chosen can be extended one time per runner (except for the first runner) by collecting every Taken Strength ball that appears inside the room the runners are teleported to after they have been the runner and run out of time. For each running timer phase there will be one Taken Strength ball inside the heart area per guardian who has been teleported inside. 1 Taken Strength when there is 1 guardian, 2 when there are 2, etc.. *All* of the Taken Strength balls per phase must be collected to reset the timer on the heart to give the current runner as close to 30 seconds as possible instead of just the base 15 seconds. The timer is reset when the last of the currently available Taken Strength balls is picked up.
One guardian will be in charge of picking up the last ball every time to avoid confusion. For the general case, whoever is the first guardian to be chosen and teleported into the room will be assigned the role of being the one to pick up the last Taken Strength ball to reset the timer. If this ends up being your job, pick a Taken Strength ball and stand close to it to "claim" it without picking it up (it is important that it is obvious which one you will pick up visually, to avoid any confusion for Zoey). If you are any other guardian than this one, kill adds but also pick up any Taken Strength ball that isn't the one being claimed by the person who will pick up last as soon as you can. You can pick up more than one, but as with the ogre encounter you can only get Taken Strength x2 before dying so don't pick up more than 2. When the current runner's countdown reaches 3 seconds (to allow for lag, etc) the person whose job it is to pick up last should grab the last remaining Taken Strength to extend the timer (all other Taken Strengths should have been picked up already by the rest of the team).
If Zoey is the first person chosen and teleported to the heart, the person teleported in second will be in charge of picking up the last Taken Strength every time once they are inside. Zoey will pick up the one and only Taken Strength that is available on the first phase at 10 or so seconds after she is teleported in (better to be safe than sorry, we don't really need the maximum amount of time to get this to work as long as nobody dies) to extend the second runner's time, but after that we'll have someone inside who can hear the callouts so they will take over the job of getting the last Taken Strength.
When Zoey or Jugg are the runner (and not the first runner, where it doesn't matter because the timer can't be extended), they will send any character to a shared Xbox One chat group we are all in at about 5 seconds left (we may need to adjust this if 5 seconds isn't enough time). This notification will be the cue for the person who is picking up the last Taken Strength to pick it up. Don't assume you still have 5 seconds to go when you see the notification, just pick it up as soon as the notification pops.
Here's a video that shows the full run from the perspective of the last person remaining as runner (so you can see where to 'slam' the heart if you are last):
Note that once you get back to the vault area, one of two doors can be open (rock or tree) at random, go into whichever one is open and then travel through the side-tunnels to get back to the 'temple' vault room, where you drop into the hole in the middle. One of the side-tunnel routes in the open room will be blocked by a huge taken blight, so take whichever one is open and just keep following side tunnels until you reach the temple room. When you reach the temple room, fall through the giant hole in the center and then run up the stairs, find the Techeuns and just touch the big circle in the center.