In ch. 5, Mr. Knightley says to Mrs. Weston that Emma taught her (as Miss Taylor) to submit to another's will and to do as she was bid. He might also have added Mr. Woodhouse's effects, I think, since Mr. Woodhouse very much liked things done exactly the right way, from a door's lock being turned, to being asked permission for (being talked into) social engagements for his daughter.
But Mr. Woodhouse was also teaching Emma, and I think her lessons will be felt by Mr. Knightley, though he may never know it. When Mr. Knightley, reading Frank Churchill's letter, agrees that he did not arrive until Miss Fairfax was in Highbury, Emma immediately pays the compliment that Mr. Knightley always suspected his lateness in arriving. She never says a word about her own doubts and resentment (on Mrs. Weston's behalf) on that score, nor that she agreed with Mr. Knightley that Frank Churchill's behavior was not what a young man's ought to be, long before their present current good understanding.
How did she learn to subsume her own vanity in her intelligence (vanity which we, and she, KNOWS she possesses), in order to flatter the man who will be the new center of her universe? By doing exactly the same thing to, and for, Mr. Woodhouse. Others, too: she watches her guests, and urges them when they need it; she listens to her sister's and brother-in-law's conversation, and intervenes when she sees any storm on the horizon; she distracts Mr. Woodhouse when Miss Bates mentions cooking pork in an "unwholesome" way; she forebears when Mr. Weston and Mr. John Knightley (in their separate ways) tax her politeness by assuming she agrees with opinions that they must have guessed she would not, had they thought rationally about what they knew of her -- she can not change anything in either case by outward displeasure, and so stays silent.
Emma, as Mr. Knightley's betrothed, instinctively takes a supporting role, still sure of her own importance, I think, but willing to fall a half-step behind and to the right, so to speak, and pretend that the perfection of Mr. Knightley is one to which she can not aspire, out of love for him, as well as actual respect. She has been practicing smoothing little matters for those she loved since she was twelve, and no doubt had some excellent pointers from Miss Taylor, as well as her own good nature, principles and sense to guide her. Mr. Knightley will still see her saucy looks, and hear her cheerful banter, and, knowing his own good judgement to be worthy of her respect, never doubt that she admires him as much as she implies.
It is kind of cute.