I used to prepare my asparagus by cutting an inch or two of the end before cooking it. This was supposed to remove the stalky part but it did not do an effective job as this would leave a fibrous, inedible part at the end.
My sister-in-law suggested a much better way of preparing asparagus: grab the asparagus from either end, bend it until it snaps and discard the firm, stalky end. This works great and you don't end up serving parts of the asparagus that are too fibrous to be eaten.