See The Spirit of Christmas Past for details on how to start the Christmas spirit quest.
Go through the portal to the future outside of Santa's Workshop to witness future Sam & Max trapped on a small island surrounded by lava. There's nothing you can do right now, so return to the present and head back to Straight Street. Go into Stinky's Diner and ask Stinky how business is. She will complain that her feet hurt. Head back to the North Pole and enter Santa's Workshop. Use the green computer to dispense a "foot bath and piranha aquarium", and then use a gift tag to send the present to Stinky. Head back to Stinky's Diner and pick up her sock from the counter. Return to the North Pole with the sock and enter Santa's Room. Put Stinky's sock into the stocking stuffer, which will fill the sock with coal. Take the coal back outside and put it in the boiler at the back of the sleigh right next to the portal to the future. The sleigh will be used to save future Sam & Max and the Spirit of Christmas Future will be satisfied.