There are a ton of different ways to cook them.
Most people start by removing the tail. I've only seen once where someone cooked the entire Lobster. I think this is done more in places where food is scarce and they try not to waste even the smallest bit.
You can see how to remove the tail here
http://floridalobstering.com/how-to/how ... obster.phpYou do not want to boil the Florida lobster first. That is how people make Maine lobster, not Florida lobster.
Grilling and baking are typically done the same way.
You can follow the directions for cooking here
http://floridalobstering.com/how-to-coo ... ster-tail/If you would like to see a video of how to cook them, you can watch this video on making a Florida lobster roll. The initial steps where the lobster is actually cooked are identical.
http://youtu.be/C-jI_v72kuE?t=38s