The asparagus should be rinsed, and the rusted endigs cut off. The green asparagus does not require any further peeling (very large, mature spears can be peeled at their very endings). The proper way of cooking by boiling, baking or grilling will cause the asparagus won't get fibrous. Instead, they should be crispy and firm. If cooked for too long they turn very soft and untasty. After cooking the green asparagus should still have an intense green colour, not light green or brown. In order to achieve the best possible results, boil the white asparagus in a salty water with a bit of sugar for 7-8 minutes (5 minutes for green) or bake it after covering with salt and pepper, and spreading some olive all over it (at 220 degrees C for 11 minutes). The asparagus can also be grilled, baked in a tin foil or baking bag, or steam-cooked. It can be served as a main course or as an addition to salads, pasta, eggs, tartes, pizzas or risotto. It can also be solely served, i.e. with sauce hollandaise poured over, fried breadcrumbs or it can be baked with parmese ham. Alternatively, it can be served in form of soups and cremes.
White asparagus is more fibrous than the green, and must be peeled (except the spearheads). Peel the asparagus with the asparagus peeler, a regular vegetable peeler or a small sharp toothless knife. Peel it downwards, starting under the spearhead. Peel carefully so that no fibres are left. Afterwards, cut the tough, lignified endings, removing around 1/3 of the spearhead. Fresh spearheads sometimes only require 2 last centimetres to be cut off, while the old ones must be shortened even by 5 cm.
The green asparagus doesn't require peeling. It is enough to just cut off the lignified endings. The most certain way to do so is to cut the 1/3 of the spearhead. Alternatively, fold the spearhead and it should break itself.