One of the most likely is the scarlet bodied wasp moth; it has the color pattern you describe and is also of a similar shape to a butterfly, being a moth. This insect is generally found in warm climates such as India.
The burnet moth also is a similar color and shape, though it can have a tint of red on its wings. It is found in the USA and could possibly be the insect you found.
The turquoise fly is not turquoise but the color you describe, this may also be the animal you came across and is also found in the States.
There are a number of insects that have this coloring, the best thing to do is to take a picture of it if you come across it again and use a reference book on insects or perhaps an internet site to compare it and see what it looks most like. This may be the easiest way to determine the type of fly it is.
Entomology is the name of the pastime of examining and collecting insects.
Books on entomology are quite easily found on the internet and Amazon has a wide selection at low prices. One of the best is the aptly titled Encyclopedia of Insects. This book offers a huge selection of insects and also very clear pictures for you to compare the insect you saw to.
The best thing to do is to compare and contrast a photo with what you saw. This will give you the best idea of what it is. It is hard to determine from only a description as the insect kingdom is so vast.