Hi Twink,
I was going to suggest contacting ACE, but see from Scummymummy's thread that you already know about them!! They are fantastic and I would certainly recommend that your friend gets their appeals leaflet and speaks to them for advice.
Difficult to comment really without knowing details of why a place wasn't offered. For example an appeal for the most local community school would be very different than an appeal for a denominational school miles away.
If there is no suggestion of maladministration then your friend needs to make the case about the benefits for her child to go to the school and highlight the particular difficulties for her child if she/he doesn't go to that school. What is it particularly about that school that is most appropriate for her child rather than another school - the appeal needs to be positive for that school rather than negative for all surrounding schools ie. Not "we want him/her to come here because all the other schools are useless". Might be true, but it won't win!
Make sure that any supporting evidence is backed up - ie if there are physical/medical/emotional reasons then try and get supporting letters from appropriate professionals. Ideally these should have been submitted with the original application, but should definately be included with the appeal.
Include all the reasons - even the ones that may seem trivial - they can always be rejected, but can't be added in afterwards.
In terms of the actual appeal itself (I don't understand how Tallulah had 3 appeals - usually there is only 1 I think) I would advise your friend to stay as calm as possible - this is usually pretty difficult, so advise her to pretend to be calm - it works just as well! Make sure she has a list of things that she wants to get across in the appeal and to tick them off if necessary as she goes. If the appeal ends and there are things that she still wants to say then she should ask to add something. You have to come away from these things feeling like you've given them your best shot.
Whatever happens with the appeal, I would advise that your friend is now trying to get her child's name down on to other school's waiting lists - as I said on Scummy's thread it does not pay to threaten to keep a child out of school unless you are in a position to actually do so. Even if she accepts a place at another school it can be turned down if the appeal is successful.
Hope that helps - let us know how she gets on