The methodology basically gives you permission to feed your child what you are eating instead of pureeing bland foods for them. The idea behind it is that they will get a taste for real foods if they are given real foods.
Another important aspect of the method is giving them the food instead of feeding it to them. For example, making matchsticks of foods so they can hold on and eat it themselves. Or "loading" a spoon and handing it to them.
"Food is fun until age one," is one of the major ideas. We basically thought of it as letting our child play with food instead of play-doh or plastic. It allowed me lots of time in the kitchen (up to an hour per meal sometimes, but all babies are different) to get prep work done, cook, or clean. We also got the satisfaction of knowing that our baby learned which foods are which at an early age.
Another leading idea is that babies have a choke reflex (we all do). But theirs is closer to the middle of their mouth when they are younger, and, as we age, it goes further back, towards and into the throat. This means that when they cough/ choke on something earlier in life, they learn how to cope with it before it is more of a danger to them. All of this means that it is likely safer to let them cough/ choke a little (as long as their face is red instead of blue, of course. Red means they are getting oxygen and blue- which we never saw, by the way- means you need to do some Baby Heimlich). They quickly learn how to cope, and how to chew and swallow properly.
This video was taken of our 10-month old son eating a peach:
He rarely gets yogurt in his hair anymore, although there was a period of time in which he loved everything dipped in yogurt.
And please don't get too scared off by the pictures. Yes, it really was this messy, and yes, it was only a phase. He learned to eat a lot cleaner as time went on, and got quite proficient with cutlery pretty early.
Here is the book. There is also a Yahoo! Group for people to support each other who are doing this, which is immensely useful, especially if you don't know anyone else who is doing it.