For example: You know how in the beginning Alvor or Gerdur allow you to take items, when talking to them. How do I do this?

I looked up the ShowGiftMenu topic in the CK wiki, but don't understand it.

The basic syntax in a dialogue fragment would be

akSpeaker.ShowGiftMenu(true)

The "true" means the player is giving the NPC items; it would be "false" if you want the player to be able to take items from the NPC. In dialogue fragments, "akSpeaker" is always available as a shorthand for the actor the player is talking to.

As the wiki page suggests, you can additionally use a formlist of either specific items or keywords to control what can be given/taken, if you want to limit that. Don't worry about where it talks about favor points, as I don't think any of that was actually implemented in Skyrim.

Thank you so much, DreamKing.