Go to the store with her and help her choose the three basic knives -- chef's, bread and paring. Or help her choose on the net. Help her choose a sharpener; a steel; a block, bar or covers, and a board. Teach her how to sharpen, maintain and store her knives. Teach her how to clean her board.
Teach her to "pinch" her chef's knife. It's an unnatural act, you'll have to convince her it's important.
Get a few good, pro-level spatulas and one or two whisks. Oxo's OK for the whisks. Get a board knife.
Get pour spouts for her oil bottles. Get oil bottles.
Teach her never to put food in a cold pan.
Teach her how to know when to turn food in a pan and how to know when to leave it alone.
Teach her to stop, taste and adjust the seasonings several times as she goes along.
Teach her how to truss and roast a chicken.
Teach her how to make fried chicken.
Teach her how to make a couple of dishes she really likes to eat, a couple of dishes she'd like to serve to a boy-friend, and a couple of dishes she'd like to serve at a party. You don't have to dumb these down.
Teach her how to check for doneness by touch, and how to use an instant read thermometer.
Teach her to keep her hair out of her face and the food when she cooks.
Teach her how to make: Pan-reductions for quick and fancy. Beurre blanc for fish. Veloute for gravies in general. Mornay for mac and cheese. If she's in or from the South, she needs to learn how to make a "cream" or "milk gravy" as well.
Teach her how to cook bacon.
Teach her how to fry an egg, make an omelette, poach an egg, scramble an egg.
Teach her to make mac and cheese without anything from Kraft.
Teach her how to make a salad that does not involve iceberg lettuce, or a knife ever touching any green. Teach her how to make an emulsion vinaigrette.
Teach her how to deal with hot liquids in the blender without baptizing the ceiling.
Teach her hot to make biscuits, pie crust, fruit pie, and basic bread.
Teach her how to make cake from a mix.
Most importantly, try to convey the idea that almost all dishes are cooked with the same basic techniques. That cooking is more about technique than recipe. And once she has the techniques she can follow any recipe.
Teach her that no matter how wrong everything goes, the worst that can happen is you call out for pizza -- and everyone loves pizza. No pressure.