A quick post to give some info about the recent Diablo 3 patch, and how to level the new legendary gems in the most efficient way!
When you first start out, you want to clear the highest torment normal rift you can do safely and quickly at a chance at a trial keystone, the initial testing seems to imply that it has a 100% droprate at T6 and 20% at T1, on a linear scale with the torment difficulties inbetween.
When you have the trial keystone, if you don't have any legendary gems, fail your trial at wave 1. This lets you start at greater rift 1 and just plow through the map in no time. The guardians typically drop 1-2 gems. Keep upgrading your rift keystone until you get the primary gem you want to level up.
When you have the gem you want to level, get a trial keystone and then set your target wave. When you finish a greater rift run you get 3 upgrade chances, and you ideally want 100% success-rate at this. To get this you need to be 10 levels above the target rank. Say you're starting out with a gem at rank 0, the target will be rank 3, which means you need a rift level 13 or greater to get 100% success chance on all your upgrades.The trial run is designed to give you a greater rift 5 levels below the wave you ended at, so if you're trying to upgrade the rank 0 gem, you want to stop at wave 18 in the trial run.
Then rinse and repeat, one normal rift, trial rift at target gem rank + 15, quickly clear greater rift, upgrade gem!