To start the quest, talk to Santa just south of the grand exchange. Santa will tell you that Jack Frost is up to something and he wants you to investigate.
(http://i.imgur.com/mTBRTcw.png)
Head to the dwarven mine on ice mountain and talk to Jack. He says he won't share his plans with you.
(http://i.imgur.com/JshCxkf.png)
There are several imps walking around the area, talk to the one called Benny. He will tell you to talk to Sir Taffy Cashien.
(http://i.imgur.com/DG7oG8S.png)
Travel to Falador park and speak to Sir Taffy Cashien, he will tell you about Jack's plan.
(http://i.imgur.com/oQ8C4Zx.png)
Go back to where Jack is and talk to him about his plan.
(http://i.imgur.com/QlYe025.png)
Head back a choice: You can choose to help Santa or Jack.
(http://i.imgur.com/tSTObwt.png)
After this, the quest is done and you will be rewarded with a christmas cracker.
(http://i.imgur.com/8PmiUSi.png) Deliveries (http://i.imgur.com/nCyhI1J.png)
You can now choose between delivering regular or dark presents with the deliveries you get from Santa.
You will get a dark christmas cracker from jack's deliveres. This cracker is exactly the same as the regular one,
so I recommend you just stick to doing regular deliveries, as it takes less time to get normal presents than it does to get dark ones.
If you need a guide for deliveries it can be found here (https://emps-world.net/forum/index.php?topic=14826.0).
Merry Christmas.