Please Help - I'm going to try and fix girlfriends hair!! (wants natural looking ash blonde but it's grey green!)

Hello,
Could someone please advise on a strategy for someone that's never colored hair before but would like to "experiment" on my girlfriend's hair? (She's willing!!!)

She recently got her hair done (went from a brassy blonde to ashy tones). Very EXPENSIVE with not so good results (green undertones and sorta greyish...the stylist said, "well that's ash"!! ...anybody know what he did wrong?)....so I'm taking the challenge of trying to fix it!

She wants a nice natural looking ash blonde (normal hair color is brown...roots are very noticeable after 1 month)

I was thinking on an approach that would take what she has now (it's lightened a bit and not quite as grey/green), and adding TONS of highlights (various shades of ash blondes down to maybe a brownish lowlite that's close to her original color to mask the new growth).

Would this be the right approach? Would it hide the grey green and be maintainable?

Does anyone have thoughts as to the colors of ash and brands to include in the mix? Can I hightlight with 3 or 4 different shades of ash simultaneously or should I do 3 or 4 separate treatments?

Does anyone have any recommendations on "how to" sites or books / videos for doing color work (highlights) at home??? I'm up for the challenge but would like some thoughts on technique, TONERS, amount of time to leave it on, why it's used, etc. and all that stuff...

Any help would be greatly appreciated! Thank you in advance!
-T