Step 1
Talk to Kaqemeex, Druid circle, northern Taverley.
Talk to Sanfew, Taverley herblore store.
Dip raw chicken, beef, bear, rat meat into Cauldron of Thunder (Taverley dungeon).
Speak to Sanfew then Kaqemeex.

Speak to Kaqemeex north of the Witch's house in Taverley. Ask him about Herblore and he will refer you to Sanfew. Sanfew is located in the Taverley Herblore shop on the second floor.

Speak to Sanfew and he will tell you that you need to collect raw rat, bear, beef, and chicken meat, and that you have to dip them into the Cauldron of Thunder (Picture).

Gather the meats and head to Taverley dungeon (south of the Herblore shop). If you are able to access Canifis, you can buy all these raw meats from Rufus' Meat Emporium for 1gp each. Otherwise, follow these instructions: collect the raw bear meat north of Falador, near Ice mountain, then get the raw chicken from Falador Castle, the raw beef from the multi-purpose farming allotment south of Falador, then finally the raw rat meat from Port Sarim. Then just go back to Falador and climb the broken fence for the shortcut back to Taverley. An alternative strategy for those without access to Canifis is to use the teleport home spell. In Lumbridge, you can find cows, chickens; near Varrock there are bears; and in the Varrock sewers, there are rats (There are also rats behind Lumbridge castle).

Go down the ladder into Taverley dungeon and head north until you reach two suits of armour. When you try to open the gate, they may come to life and attack you. Once you have passed the suits of armour, go in and dip the meats into the cauldron. Return to Sanfew, who'll tell you to visit Kaqemeex. Go back to the Druid circle and speak to Kaqemeex to collect your reward and learn of Herblore.