Note that you can learn to fly in Northrend already at level 68, so make sure to learn this from a mount trainer to increase the leveling speed by a whole lot!
Check out all parts of the leveling guide:
Part 1) Level 1 - 58 / vanilla leveling guide.
Part 2) Level 58 - 70 / The Burning Crusade leveling guide.
Part 3) Level 70 - 80 / Wrath of the Lich King leveling guide.
Part 4) Level 80 - 85 / Cataclysm leveling guide.
Part 5) Level 85 - 90 / Mists of Pandaria leveling guide.
Part 6) Level 90 - 100 / Warlords of Draenor leveling guide.
Part 7) Level 100 - 100 / Legion leveling guide.
Level 70 - 80For this part of the leveling journey, you want to do some quests. Keep doing quests that match your level, and don't be afraid to skip out half of the zone once you outlevel it. Always stick with a zone that matches your level!
Always fly to the quest objectives, do them and return to the quest giver. Don't bother killing non-required mobs, and just focus on the quests.
While question, sign up for random dungeons, and make sure to complete each dungeon at least once, because the quest experience rewards are amazing. If you prefer to quest instead of doing dungeons, you should still do each dungeon once for the quest rewards.
If you have a high-level friend that can help you, head to the Champion of Anguish questchain in Zul'Drak. This is the area style quests that gives a huge amount of experience upon doing it, and it is extremely fast with a level 110 to help you do it. Don't bother with this part if you play solo.