Artichokes are sold at the grocery store in the fresh produce section. Artichokes are in season from March to June and in September and October. When artichokes are in season, they will be much larger, and fresher at the store. When shopping for an artichoke, I have found that the best ones are very large, have rounded leaves instead of very pointy leaves, are round in shape, and have a thicker stem with a large base (where the heart is). The greener the better. I try to avoid the artichokes that are already starting to get a little dry and brown.