Slayer is trained by killing specifically assigned enemies.

/Skills GetTask – Get a new Slayer task. This is what you need to kill.

/Skills Task – Check your current task

/Skills ClearTask – Pay $1000 to clear your task. This will clear your streak.

A task might be to kill, for example, 64 chickens. Each chicken you kill will earn XP. Completing the task will add to your slayer streak.
Earning higher slayer streaks will give you large amounts of XP.

There are special books from the rewards shop and TH which allows you to clear a task without resetting your streak.

Level 100 Slayer will make it so your armour will never break.