with her weight & height, sounds to me as if she may be a bit 'skinny fat'. She certainly is not over weight - sounds as if she just needs to BUILD some muscle in order to be 'toned' b/c how can you have "muscle tone" (visible, firm muscles) without the muscle?! Right?
Is she scared of bulking up? Getting her over that fear is goal #1! most ppl don't put much hard work into their workouts (I'm an aerobics instructor - been leading people (non -athlete ppl) in workouts for 4 years) If she is AFRAID of "getting big" then she is certainly not going to put forth effort. I highly recommend the sticky article 'reasons why women need strength training' at the top of this board. Should clear up any fears.
Otherwise - diet - clean, close to nature, UNPROCESSED CARBS (lose the pasta), lots of veggies, lean protein, fruit, healthy fats. 6 small mini meals a day, lots of water. She can try fitday.com to get an idea how her diet is - i.e. total caloric intake, % split amount carbs, fat & pro- just check up on it, the #'s aren't always right. Small changes bit by bit are often helpful in making a complete, FINAL transition to a really healthy diet. -> this is NOT for the short term!
As for a gym, she can spend only about $25 & get an awesome set of adjustable dumbells & have all the weights she needs!!! She can use her aerobics step as a bench to lay & sit on - she can even turn it into an incline & decline bench (with the risers on the step).