There is no easy way to train slayer like there is in other skills (unless you have enough RS Gold to buy a cannon). No matter what you do, you are always going to have to fight a large number of monsters.
The Shilo Slayer master gives out tasks of up to 199 monsters per task; most of the tasks are pretty hard to finish at low levels, so high combat level and good melee stats are recommended. If you are an average to high-level player, try to use the Canifis, Edgeville and Zanaris slayer masters.
Cave Horrors have recently found their way into Mos Le'harmless, bringing with them a Black mask. To gain access to the Mos Le'harmless Dungeon, you must have completed Rum Deal and Cabin Fever - you will also need a lantern to guide yourself through the dark caves. This mask gives a +15% boost to your attack and strength levels, however, only when fighting the monsters you have been assigned to as a Slayer task. The number at the end of the name represents the number of times a spell will shoot from the mask and lower any of your opponents' defense by 10%. When the number reaches 0, the mask will no longer shoot spells, but will retain its strength and attack-boosting abilities. Make sure that you wear a Witchwood icon, else you will be dealt 9 damage every few seconds.
If you're a skiller wanting to train slayer, it's possible but difficult. You will need many rings of recoil. Turn off auto-retaliate, bring lots of food, and do Burthorpe tasks. This way, the monsters will be lower-leveled and you won't receive any combat experience. Keep in mind that this is tedious, but besides experience lamps, it's the only way to train Slayer on a skiller.