In RWI the letter C is not 'cuh'! And T is not tuh --
C is more like a short sharp C! sound, T is more like a short sharp T! sound -- both hardly leave your mouth. P is a very soft puh sound, H is a very soft huh sound, (like panting breath) etc. S is a sssssssss sound like a snake.
I liked yogabird's explanation about Fred speak, otherwise, but not sure the sounds she said are at all right.
In RWI the children learn the sounds / letter shapes with a picture that has that sound, like 'r' (said 'urrr') for robot. And there are pictures with more advanced sounds/groups, so a picture of mum hoarding cakes and the children saying "That's not Fair!" for the 'air' sound.
Apparently you can go to the RWI website and there is a video showing all the sounds.
RWI has a good reputation, misdee's girls are on it (search for posts by her, or for the name 'Ruth Miskin').
DS2 is in reception on RWI, and the school did several sessions explaining to parents what it was about. DD is on a level of RWI, where they work on more complex letter arrangements (eg. 'u-e' or 'tious'). Working intensely in groups sorted by abilty, with a partner, is an important part of RWI.
I think RWI is quite prescriptive and some teachers balk at it for that reason, but it gets good results and the kids like it (esp. "poo at the zoo" ).