Create a new game and check the map for the following bounties:
Miser's Will (Act V - very rare) - Westmarch Commons - could take a while to find the Miser's Hovel
Miner's Gold (Act II - common) - Howling Plateau - need to be alive to get the experience when the event ends. Either keep moving and avoiding enemies, or respawn right before it ends. If you can, open the resplendent chest to get some loot so that you are tankier in future runs.
Jar of Souls and The Matriarch's Bones (Act I - somewhat common) - Cemetery of the Forsaken - the Matriarch's Bones can be completed without killing the Ghost. Just ignore him and click for the crypt to end the quest.
This method is even better in a party (since there are more targets for enemies, less chance of dying), with each player creating their own game and inviting others once the quests are found. It also makes it more likely for the party to find the Miser's Will event, which grants more experience than the others.
Mind that this method has a few cons:
It is somewhat boring, as you aren't really fighting, just avoiding enemies and collecting the bounty reward.
You will die often, so it's not suitable for Hardcore (unlike the tips from the previous video).
You will get most of the experience from Miner's Gold, and there's a catch with that event - if you're dead when it ends, you get no experience (unlike the other 3 events which require you to "activate" something to get the reward).
You will barely collect any materials (pre-level-60), almost no gold (for lvl 70 enchants), and less Rift Keystones and Blood Shards than through normal leveling.
Note that in the VOD previously acquired Gold was used to buy gear from vendors (for improved Toughness), which is needed to survive and get the experience in the Miner's Gold event. That would result in even less gold once the player reaches level 70.
Remaking games over and over again (to check for the events) could be problematic for players who have disconnect issues, or if Blizzard servers are overwhelmed by too many users.