Rinse the artichokes under running water or in a sink of cold water. Set out a large bowl of cold water and add about 3 tablespoons lemon juice (juice of 1 large lemon) or vinegar. Cut off the base of each artichoke right where the stem comes out of the leaves. Drop cut artichokes into the lemon water as you work to keep them from discoloring.
Remove the leaves all around the base by peeling back and snapping off until you reach leaves that are yellow at the bottom. Again, keep the cut artichokes in the water as you work.Cut off top 1/3 of leaves (green portion) and discard. If you wish, trim off any remaining green from base of artichoke. Remember to put the cut artichokes back in the lemon water.
Leave artichokes whole if very small, or cut in halves or quarters. Keep in water until ready to cook.