If you know what works for you, it is a good bet that it will work for her too.
I would teach her to squat properly (at least parallel, not those 1/4 squats that people do on smith machines). If you know how and are comfortable with it, I would teach her to deadlift. I would also encourage her to do split squats (you know with the non-working leg up on the bench behind her) as well as lunges, leg extensions and leg curls.
She’ll have to rearrange her running in order to be able to put in some good work on her legs and to have time for recovery.
I’d suggest that she start training in the 3 sets of 10 reps range. Make sure that she struggles with the last rep or it is too light. Try something like:
Day 2 (not the next day, just the next time she trains)
Lunges (make sure that knee touches the ground! no half lunges here!)
Step ups (can hold dumbbells once her balance improves)
I’d love to see her do some upper body work too, but she may have to be coaxed into that if she thinks her only problem area is her lower body. She’ll love the tightness that she’ll see/feel all over after she’s been doing this for a month or so.
Now here is the trick to results, she has to progress. If she tries out say, 45lbs on the leg extension machine and feels pretty comfortable doing 3 sets of 10, then she absolutely has to go up in weight next time. You will not get anywhere if you use the same weight from week to week. you have to challenge your body and give it a reason to grow stronger muscles. Even if she can only get 8 reps the next time, it is very important that she try to add weight whenever she can.
After two weeks of 3x10, I would try mixing up her sets and reps. Try out 4 sets of 6 or 5 sets of 5. I personally prefer 5x5 because it allows you to lift heavier weight than a 3x10 would. You lift heavier for shorter time and therefore progress faster.