There are basically two fast and easy ways to level up in season 7: 1) do rifts with a full group, or 2) chain kill is Fields of Misery Act 1.
Chainkilling speed levelingChainkilling monsters in Act 1 Fields of Misery is a little bit faster than doing rifts, but has a few downsides as well. The biggest problem is that you do not have any gear or gold once you reach level 70, so doing the journey needed to get the free set is a lot harder than if you level up in rifts.
To properly chainkill you also need to play as a Witch Doctor, and you cast DoTs on all the enemies in Fields of Misery. This will get you chainkills with 400+ monsters, and each run gives you a few levels.
With this method you can reach level 70 in a little under two hours! See the video below for a guide on which talents to pick etc.
The nice part about this method is that it is also viable on hardcore, so this is an easy method to get to 70 on hardcore difficulty!
Rift speed levelingThe other method is easier for most people, and it is speedclearing rifts with a group of four people. Finding three others who wants to speedclear with you is the best way, but it can also be done in public groups, but this will be slower due to not all people being 100 % focused on clearing it as fast as possible.
With a good four man group you can reach level 70 in less than two hours, so it's not really any slower than chainkilling. In public groups you should expect to use between 3 and 4 hours total, depending on the groups you play with.
Either way, do be able to do it as fast as possible you should practice on a new character a few times to get the hang of it. Plan which talents to use at what levels, so you don't need to spend time on that after the season launches.
If you want to go for the chainkill method, check out the YouTube video by Desolacer to learn how to do it.
Get boostedIf you are a few days late to the party, another good strategy is to get boosted. There are lots of boosting communities in both US and EU, so just check out the public communities, join one as ask nicely for a quick boost. This should take less than 20 minutes with a decent booster.
Good luck with season 7!