Step 1) Talk to vanaka at Edgevill. (::home or :: pk > Edge)

Step 2) Do your task. Ask him for one and he will give you one.

****Here are some details on slayer task monsters, That i prefer to kill*****

Also look at the spoilers for more detail on the monsters.
MONSTER LIST

Basilisks : Level 61

Green Dragons : Level 79

Hill Giants : Level 28

Crocodiles : Level 63
EXPS
*Spoiler*

Woman - 105 exp

Man - 105 exp

Giant rat - 300 exp

Goblin - 75 exp

Rock crab - 750 exp

Ghost - 375 exp

Skeleton - 435 exp

Deadly red spider - 540 exp

Black knight - 630 exp

Hobgoblin - 750 exp

Hero - 1245 exp

Daganoth - 1065 exp

Jelly - 1125 exp

Green dragon - 1350 exp

Turoth - 1800 exp

Elf warrior - 3000 exp

Dust devil - 1575 exp

TzHaar Mej - 3000 exp

Mithril dragon - 7500 exp

Kree' arra - 15000 exp

K'ril Tsutaroth - 15000 exp

Hill giants - 1,800 exp

TzHaar xil - 3,000 exp

Kalphite Queen - 4,500 exp

Chaos druid - 300 exp

Moss giant - 1,800 exp

Daganoth supreme - 4,500 exp

Daganoth rex - 4,500 exp

Daganoth prime - 4,500 exp

Dungeon rat - 180 exp

Knight of Ardougne - 780 exp

Hellhound - 1,740 exp

Gargoyle - 2,325 exp

Wyvern - 11,125 exp

Gnome - 225 exp

Possessed priest - 1,350 exp

Guard - 330 exp

Crocodiles - 5250 exp

Kalphite soldier - 1350 exp

Corporal beast - 15000 exp

Greater demon - 15000 exp

Nechryael - 15000 exp

Werewolf - 900 exp

Ice warrior - 900 exp

Battle mage - 1950 exp

Count Draynor - 2250 exp

Scorpion - 4500 exp

Dark Beast - 3750 exp

Abyssal Demon - 3750 exp

You can earn the slayer helm from Vanaka at 50 slayer points, here are the stats

No Stats for Attack bonuses.

Defense bonuses :

Stab : +30

Slash : +32

Crush : +27

Magic : +0

Range : +30

*****Also you can purchase a slayer gem, trade him and its 1 gp.*****
There will be more updated monsters in the future.