We can get the good doctor's origins in a number of ways, but my recommendations are:

Watch the Doctor Strange animated feature (available on Netflix instant streaming at the time of this posting)

Read Strange (2004) also known as Doctor Strange: Beginnings and Endings

Beginnings and Endings shows a nicer look at the doctor before turning him into the douche-bag surgeon he was. It also has the confusing inclusion of Clea, who is in actuality Strange's former apprentice (more on that in the next entry). Both depict the doctor's "fall from grace" as an accident humbles the arrogant jerk. He then seeks out someone to heal his injured hands, which eventually leads him to the Ancient One, the Sorcerer Supreme. Later, another apprentice betrays them both and this leads to Doctor Strange becoming Sorcerer Supreme.

Honestly, I recommend doing both if you can, but either one will do.