I went with a group of 12, so a bit smaller, but got lots of advice on the boards from people with 15+ . There is no group reservation number or anything and they said no need to try reserving for 3 groups of 6 or anything like that. Book your total group and each restaurant will determine whether they need separate tables. I liked using the phone vs online because I just felt like it's easier for me to consult my notes and ask questions while the CM is doing all the computer clicking and checking. We also had one ADR per day together. Here's where we ate:
CRT lunch - 2 tables side by side with half booth half chairs. There was a third table in this area that I bet would be used all together to seat 18 - you end up being a big arc of tables along the curved wall.
BOG lunch - technically counter service, so you find your own tables
Coral Reef in Epcot - 2 tables side-by-side
Boma in Animal Kingdom Lodge - all 12 at one table. Kind of a weird kidney-shaped table. I don't know if they have alcoves/rooms for larger groups or if you would just be seated near one another - this shape table definitely couldn't be pushed together
Hollywood & Vine in DHS - 2 rectangular tables of 6 side by side. We were more separate here than the others, the tables weren't end-to-end or anything, so we could have been two parties of strangers near each other.
Chef Mickey - pretty similar to CRT - an arc-shaped booth on one side with chairs opposite. There was a 3rd (and maybe 4th?) table here, so it could have been a bigger group. Other areas had rectangular tables, so perhaps groups would push those together
Akershus in a Epcot - 2tables together to make one long.
There really was no secret to it, despite my also assuming there would be.
ETA: definitely make your ADRs for the full number. It is easy to decrease your group size later if needed and difficult to increase. As long as at least one person honors your reservation, you are not charged the no-show fee for anyone (although it is a nice courtesy to release those extras if you know in advance). Last, are you on the dining plan? If so, you have no pre-payment on your reservations. If not, Cinderella's Royal table (along with dinner shows like Hoop de Doo and The Luau at the Poly ) require pre-payment in full at time of reservation ($$$!!). If you even think you'll want the plan, you can put it on your reservation, avoid the pre-payment, then do all the math based on your actual chosen restaurants - you can drop the dining plan from your resort reservation if need be with no effect on your dining reservations.
