Runescape Slayer rewards?
In order to get points for finishing slayer tasks, you must first complete the quest Smoking KIlls. After that, you gain slayer points every time you kill the last monster in a task, starting from the fifth task completed in a row (that is, without discarding a task). You get different amounts of points depending on which slayer master you got the task from (information from this page):
- Mazchna - 1 points
- Vannaka - 4 points
- Chaeldar - 10 points
- Sumona - 12 points
- Duradel - 15 points
- Kuradal - 18 points
You also get 5X points after your 10th task completed in a row and 15X points after your 50th task completed in a row.
As of 2014, the mechanics for rewarding slayer points has changed a bit and thus the accepted answer is no longer true.
Slayer points can be earned from a few different sources such as completing Slayer assignments or a special challenge from any Slayer Master bar Turael and Spria, by trading in completed Tuska masks, or completing contracts on the Arc assigned by Ling
The smoking kills quest is no longer required to start earning points, it now instead doubles the amount of points gained per task. The values are below and assume the player has completed the quest. Players still earn 5x the points for every 10th task and 15x for every 50th task.
- Turael or Spria - 0
- Mazchna or Achtryn - 2
- Vannaka - 4
- Chaeldar - 10
- Sumona - 12
- Duradel or Lapalok - 15
- Kuradal - 18
- Morvran - 20
See the Runescape Wiki page on Slayer Points for more information.