1.
why, how come
Used to ask for the reason or cause of something. Slightly more casual than なぜ.
2.
how (by what means)
Asks how someone managed or knows something (どうしてわかったの？). To ask for directions or the steps of a method, modern Japanese uses どうやって; どうして in that use sounds old-fashioned.
どうしてわかったの？
How did you figure it out?
どうして is used to ask "why" (reason) or "how" (method).
Usage
1. Why (reason): どうして来なかったの？ (Why didn't you come?)
2. How (by what means): どうしてわかったの？ (How did you know?). To ask the way or the steps, use どうやって: どうやって行けばいい？ (How should I get there?)
Typically answered with から (because) or ので (since).