In it's simplest terms, a low GI diet is one that focuses on complex carbs and avoids simple carbs that can spike your blood sugar levels.
Examples of complex carbs are whole grains, beans, and vegetables. They're minimally processed and often have lots of fiber which helps keep you full for a longer time. Many fruits are also low glycemic, such as apples, oranges, and berries.
Simple carbs are sugars in all forms, refined grains, and processed products made from them. Some people think of them as "the white stuff": white bread, white rice, white flour, sugar etc.
I don't follow a "name" diet but do incorporate the ideas of the low GI diet into my eating plan and have found it to be an effective way to lose weight and maintain with hypothyroidism. Plus it's a very healthy way to eat generally! The carbs that I eat are oatmeal, one piece of fruit/day, occasionally brown rice and lots of veggies.
If I eat sugar or other refined carbs now, it's like taking a sleeping pill and I feel horrible for a day. Plus I bloat up with water retention. So I'm happy sticking with low GI eating.
The South Beach Diet is a low GI diet and I've seen a book called the GI Diet (though I haven't read it so can't give you an opinion). If you want to check out the South Beach Diet, we have a SBD forum here called "Fat Chicks On The Beach" and they have a lot of useful info there.
Hope that helps!