1.) Improving Your Dark Arts
Speak to Hetty and tell her that you are in search of a quest. She asks if you would like to improve on your dark arts. Tell her yes. She will then reply that she will make a potion for you and she will need four things: an eye of newt, a rat's tail, an onion, and a piece of burnt meat.
Head northeast of Hetty's house until you reach Betty's Magic Emporium.
Trade Betty and purchase an eye of newt 
for 3gp.
For the meat you have a few options. If you are willing, walk south to the food store run by Wydin and purchase some raw beef for 59gp. If you don't want to spend the money head southwest till you reach the giant rats. Kill a rat and pick up the raw meat. The building south of the jewelry store has a range. Use the meat on the range; if you successfully cooked the meat then use the meat on the range again to burn it. 
Grab an onion 
from Fred the Farmers garden.
Just outside of Hetty's house are some level-1 rats. Kill one and pick up the rat's tail. 
Go in to Hetty's house and tell her you have found all the ingredients that she needs; hand them over. She will put all the ingredients in the cauldron and then tell you to drink from it. Drink from it and....
