If the asparagus spears that you take home from the supermarket are especially thick, it is highly recommended that you peel them so that they cook evenly. This is especially important if the bottom is significantly thicker than the top of the spear. Usually you will only need to peel very tough asparagus spears before cooking it, though some people decide to do it even when it is not very tough or uneven at the ends.
When you are going about peeling your asparagus it will be important to lay it down on a flat surface so that it doesn’t snap when you are doing this. It would also be a good idea to thoroughly wash your asparagus before cooking it, just so you will be able to get all of the dust and particulates off of it.