Start by cleaning and filleting the anchovies. Remove the heads, and then clean out the innards by scraping your thumb along the inside of the fish. Make sure to remove the spine. Rinse the fish in cold water and pat dry with paper towels. *In Spain, we often keep the spine in tact and eat it for the calcium and crunch. Feel free to do the same if your anchovies are small enough!
On a large plate, combine the flour and salt and mix with your hands. One at a time, roll the anchovies in the flour mixture, coating evenly on all sides.
Place a medium-sized skillet over medium heat and add olive oil to a depth of half an inch. Before the oil starts to smoke (when it starts to shine), start frying the anchovies a few at a time, being careful not to crowd them in the pan. Get them golden brown on each side, about 1 minute per side.
Remove from the oil with a slotted spoon and place on a plate lined with paper towels.
Season with a pinch of sea salt and serve hot, garnished with lemon wedges.