How do you trigger the cooking lesson with Undyne?

Solution 1:

Expect spoilers as this pertains to parts of the story.

There are four prerequisites for doing the Undyne Cooking Lesson event.

They are:

• Finished the game once: You must have gone through the game with the neutral route before you can attempt to do this at all.
• Befriend Papyrus: If Papyrus calls you and suggests that you and Undyne should hang out, then you have befriended him.
• Save Undyne: Pour water on Undyne after she passes out in Hotlands. She will get up, look around, and walk away back into Waterfall after you have done this.
• Have 0 EXP: You can not trigger this event if you have gained any amount of EXP.

Once all three of those have been met, you can go to her house and talk to Papyrus, and the event will begin.

These are the three prerequisites according to the Undyne Page on the Undertale Wiki, under the area tagged "True Pacifist Route."