How I eat a lobster:
First, remove the tail and claws. Set them aside. If the lobster is just out of the steamer (and if it isn’t, why are you eating cold lobster?) they’re too hot to eat at this point anyway. If removing the tail revealed roe, eat it. Roe is yummy.
Remove the legs one at a time. Break them into segments, and extract the sliver of meat from each one with a lobster fork. There’s not much there, but I don’t waste lobster.
Separate and discard the upper half of the main body shell from the part of the body where the legs were attached. Discard the upper shell and the ‘face’. Optionally, eat some of the tomally. It’s not my favorite bit, but it is perfectly edible. Discard the gills and stomach.
At the base of each leg is a significant piece of meat encased in shell. Extract and eat each of those with a lobster fork.
By now the tail and claws are cool enough to eat. I like to eat the claws first, then the tail, but that’s a matter of personal choice. The tail meat can be extracted in a single piece if you first break off the little flipper-things at the rear end of the tail, and then bend the tail back against the way it normally curves to detach the meat from the inside of the shell.