First, visit any trainer in the main cities of old Azeroth - just ask a guard, and learn Apprentice Herbalism.
[Peacebloom], [Silverleaf], [Earthroot]
Basically just every starter zone, they are filled with Herbs.
Learn Herbalism Journeyman.
[Mageroyal], [Briarthorn], [Stranglekelp]
When you reach 150, go to your trainer and learn Herbalism Expert.
[Bruiseweed], [Wild Steelbloom], [Kingsblood], [Stranglekelp], [Liferoot]
Learn Herbalism Artisan.
[Kingsblood], [Liferoot], [Fadeleaf], [Khadgar's Whisker], [Goldthorn]
If you are not on a PvE server, and you are not level 70 yet. Don't go to Stranglethorn Vale. It was filled with level 70 players when I was powerleveling my herbalism last time, and this is not a PvP guide.
After 245 you can pick up Ghost Mushrooms in the caves too.
[Sungrass], [Gromsblood], [Golden Sansam], [Dreamfoil], [Mountain Silversage], [Plaguebloom]
Go to Outland and learn Herbalism Master.
[Ragveil], [Flame Cap], [Terrocone], [Felweed], [Dreaming Glory]
Go to Northrend and learn Herbalism Grand Master.
Howling Fjord - [Goldclover]
Sholazar Basin - [Goldclover], [Adder's Tongue]
The Storm Peaks - [Lichbloom], [Icethorn]