To prepare asparagus the first thing you need to do is remove the woody ends. A quick and easy way to do this is to hold either end of the stalk and gently bend. It will snap in its natural breaking point. This is by far the easiest way and what I usually do.
You can also trim the ends with a knife. Find the place where the pale part of the stalk turns green and cut at that point.
Finally, you can also cut the bottom inch from the stems and then peel around the bottom of the stem where it is paler using a speed peeler. This will actually help retain more of the asparagus rather than wasting it.
Whatever method you use, you don't need to throw away the ends of the asparagus. You can freeze them and collect a bunch over time, and then use them to make asparagus soup.