I'll just cut to the chase. I want to have an encounter, where the player activates a terminal. Once the player is finished with the terminal, a certain NPC approaches the player and engages a conversation, walks off, and disappears. Would someone tell me how to do this?

Make a quest, add a few stages to it, just the numbers is fine for this.
Make your NPC and give it an Editor Reference ID
In the results script portion of the terminal choice that calls the NPC, set the stage of your quest stage to some value and call an evp on your NPC
Give your NPC a dialogue package and add a condition that the quest stage be equal to the value you set on the terminal
Check out the tutorial in my sig to learn how to make a forced greet and initiate a conversation with the player
Give your NPC a second AI package, this time make it a travel package and give it a condition that the quest stage is equal to a different value then the one used for the dialogue package.
In the results script of the dialogue topic that ends the conversation with the player set the quest stage to this new value and slap another evp on your NPC.
Your NPC will travel to the destination you picked in the travel package.