A blooming onion is a deep fried onion which opens up during frying to resemble a flower.
Obviously, I start with a giant onion. How do I cut it?
This is best described with images.
Alternatively, if you're willing to drop a few hundred dollars, you can buy a bloomin' onion cutter. This is what restaurants use. There are cheaper alternatives, but I can't vouch for their quality or ease of use.