Answer:
It depends. A slayer of what? Dragons? Vampires? Demons? In some cases slayers are trained from birth as it was a family's duty and honor.
In other cases some were chosen randomly by fate to be born with 'gifts' that allowed them to battle such beings.
And then last there are those who are trained or self taught merely because they feel they should take on the burnden of defeating 'evil'. These types of people have either experienced a tramatic incident in their past that drives them in vengeance to spike out and slayer the beings that caused the trama. Or. Simply that person thinks it's a 'cool' profession that suits their taste e.g. thrill seeking, adventure, supernatural.
Hope this helps you.