Rinse your calamari well to remove the solution it was packed in. Feel for any cartilage and remove it. (If you are starting with tubular calamari, slice it into rings two inches wide. If the tentacles are attached, cut them off and remove any cartilage. Keep the tentacles to cook with the rings.)
Pat the calamari dry with paper towels and set them on a sheet pan lined with more paper towels.
Add a thick layer of flour to another sheet pan. Dredge the calamari in the flour, in batches if necessary. Make sure to get some flour inside the rings, to absorb any excess moisture.
Add the oil to your frying pan and heat it on the stove, on high. (If making several batches, you may want to use two frying pans.)
Fill a small brown lunch bag halfway with clean, dry flour. Add the flour-dredged calamari to the bag, fold it closed, and shake. This second coating of flour is to ensure the calamari is dry. (If you don't have a paper bag, add clean, dry flour to a dinner plate and dredge the calamari in that.)
When your pan is sizzling hot, gently drop the calamari into the oil in a single layer. (You can use a fork, if you wish, but I found it easier to use my hands.) If your calamari is small, it might be fully submerged in the oil, and you won't need to flip it. Otherwise, the oil will cover the calamari halfway, and you can use a slotted plastic spoon to flip them over when the first side is golden.
Cook the calamari until they are golden and crispy on the outside (it will take a few minutes.) Remove the cooked pieces with a slotted spoon and place them on a paper-towel-lined platter or sheet pan to absorb the oil. Continue frying the calamari in batches. (If you are making more than a pound, you will need to change out your oil when the pan gets too filled with excess flour.)
Add salt and pepper to taste and serve with lemon wedges. If not serving them right away, you can cover the fried calamari with foil and keep them in the oven on warm, no more than an hour, until you are ready to eat. Store leftovers in the refrigerator for up to three days.
It just takes a few minutes to fry each piece of calamari, but you'll need about 30 minutes to fry all of it in batches. If making three or more pounds of calamari, it helps to have two frying pans going at the same time.