I'm working on a quest where someone who has been giving you objectives is revealed to be the enemy, so the final objective is to kill him. How do I add a script to the dialogue that causes him to enter into combat with me after the player has spoken to him? I'm assuming it has something to do with Actor StartCombat when SetStage reaches a given amount, but I don't know how to implement that. Any suggestions? I've been able to make the entire quest up to this point work to perfection.

Yes you are correct in that you'll need to use the "StartCombat" command. I haven't tested it, but in the last line of dialogue where you want him to begin attacking you, try this command in the result papyrus script box:
StartCombat(Game.GetPlayer())