The following video goes over some main tips on how you can get to Level 70 quickly in Season 6.
Here is a list of tips from the video:
#1. Take Followers Weapon: In the early stages of the game using your follower's weapon will actually give you a big damage boost. This will allow you to defeat monsters more quickly, finish quests more quickly and ultimately level up faster.
#2. Use a Pet that Collects Gold: You will need gold to craft new weapons and armor in order to progress more quickly through the game. Get a pet that collects gold to help you save time.
#3. Play on Master Difficulty: Look for one of three bounties to complete. Choose either kill Zoltun Kulle (Act 2), kill Maghda (Act 2) or Cursed Cellar (Act 1). These are quick bounty turn-ins.
#4. Play on Hard Difficulty- From here on out lower the difficulty to hard and play on Hard until you reach 70.
#5. Collect + Damage Rings and Amulets: Check merchants for these items to get a significant damage boost.
#6. Get Leoric's Crown: Once obtained socket it with the highest grade Ruby to get bonus EXP. Include a Ruby in your weapon as well.
#7. Look for Items with +XP: Many set items provide a % EXP bonus that you will need.
#8. After Level 70: Once you hit Level 70 keep progressing and two set items will automatically be sent to your mailbox specific to your Class.
#9. Complete Greater Rifts: Progress through the higher level Rifts until you can complete a Level 20 Rift. By this time you should have the full gear set.