This can be completed in either adventure or story mode. Simply level up and this will unlock when you hit 70.
This can also be boosted if you have a friend with a geared level 70 character. Have them invite you to their game on the highest difficulty they can manage and you should be 70 in no time.
If this is your first character and you can't get a boost then you will need to complete story mode as adventure doesn't unlock until you complete the campaign for the first time. Make sure to equip a ruby in your helm as soon as you get or craft a socketed one and keep updating the gem to the best you have access to. Only replace the helm when you get a better socketed one, +n XP is more valuable than the majority of other stats.
If this is not your first character then there are a few things you can do to speed up your subsequent character's levelling.
Craft a
Hellfire Ring for the XP boost that gives. It can be equipped at any level and will give a huge stats boost on a low level character. Make sure you craft the Reaper Of Souls version of this item (it will have the affix that has a chance to engulf the ground in lava). The older version is ok too but the Reaper Of Souls version has level 70 stats so more bang for your buck.
Do greater rifts and level a
Gem Of Ease to rank 25. Socket that in a level 70 weapon and it will set the level requirement to 1 so that your new character can equip it. Apart from this being a huge stats boost it also gives a nice +1750 XP per kill (or more if the gem is higher than level 25). A level 70 weapon on a new character is frankly game breaking so ratchet up the difficulty as high as you can until you start dying (probably around the late 60s) then tone it down slightly towards the end.
Any socketed gear you get can have the highest level gems you have access to equipped in them. Remember to put a dirty great big ruby in your helm for the XP boost. As for the other gems you can either stack amethysts for the HP boost to survive in your elevated difficulty settings or you can go glass cannon and equip the appropriate DPS gems instead, that would be topaz for your Necromancer. If you don't have the gem of ease mentioned above I'd go for a ruby gem in your weapon.
You can even reforge secondary stats on items to reduce the level requirement from 70 to 50. To be quite honest though, it's really not worth it. Obviously equipping level 70 gear at 50 is great and will make you almost godlike but I don't think it's worth the time it would take to collect all the pieces for a character and reforge the level required reduction onto them.
Happy levelling!