Buy asparagus spears that look firm, not shriveled; the ends should be moist. The thickness of the spear is a matter of personal preference and market availability. To prepare asparagus, snap off the base of the spear where it breaks naturally. Remove the triangular leaves if they are harboring grit. You can peel the lower portion of thick stems if they seem tough. To serve as a side dish, steam or boil the spears until they are fork-tender.