Hence the reason why I am asking about the system, and people seem to have difficulty explaining it. How many keystones do I get and how are they upgraded? If I get to a level 44+ rift (which was the limit a week or so ago that people were pushing) and fail, do I get to continue in that same level (or, at least around that level) OR do I have to start over from level 1?
Because, if it is level 1, there is absolutely zero point in even bothering.
You do regular rifts in torment difficulty and the rift guardians have a chance to drop a keystone of trials. (on t6 the drop rate is 100%)
When you have a keystone of trials you use it on the obelisk just like you would a normal rift fragment. In this map you will fight waves of enemies, and you have a timer with each wave. The goal is to kill all of the enemies before the timer expires. Once you fail to kill a wave within the time limit your trial is over and you are given a greater rift keystone of a level that is appropriate for your character.
The greater rift keystone will have a number displayed on it, that is the level of greater rift it will open when used at the obelisk. If you manage to kill a greater rift guardian within the time limit you have an npc that spawns and he gives you 2 choices, either upgrade a legendary gem, or upgrade your keystone. How much your keystone gets upgraded depends on how much time was left on the timer when you killed the greater rift guardian. If the time left is under 4:30 it will only go up 1 level.
Once you use a greater rift keystone it is used, the only way to get it back is to upgrade it after killing a greater rift guardian. If you fail a greater rift you need to use a keystone of trials again to get a new greater rift keystone. (every time you use a keystone of trials you get a greater rift keystone based on the amount of waves you kill)
I really don't think it is possible to go into anymore detail. I hope this helps.
EDIT: Some additional details:
If you fail a greater rift you can still upgrade legendary gems.
The chance to successfully upgrade a gem is determined by both the greater rift level, and the level of the gem. If the greater rift level is 10 levels or more above the gem level it is a 100% chance.
You have 3 rolls to upgrade a gem, and you can switch which gem to upgrade with each roll.
Here is a chart for the upgrade chance for gems.