Slayer Master- Found in Edgeville Dungeon.
To start a slayer task, talk to the slayer master. You will be assigned to kill a certain number of monsters anywhere around the server. You can check how many monsters you have left to kill by clicking the slayer skill under the skills tabs.
Note - Vannaka (The Slayer Master) can be found East of the Lumbridge Yak fields right above the Dungeoneering NPC.