One of the most healthy way to cook vegetables is to steam them. Even when you microwave them, you destroy some of their important antioxidant properties.
In order to steam veggies, you need a steamer pot. This is actually a three piece item. First, you have a regular sauce-pan, in which you boil the water. Into this you sit the steamer pan. This is like a smaller sauce pan but has holes in the bottom of the pan. It holds the food and sits in the top of the bigger sauce pan, keeping the food up away from the water. That way when the water boils, only the steam rises up through the holes and cooks the food. Finally, there's a lid, to help keep the steam in.
You can either cut the food up into little pieces to help it cook thoroughly, or cook it whole if you want to have a nice presentation. You want to bring the water to boiling, and then add on the steamer pan with veggies. Keep the stove on during the next minutes or so, while the steam boils away and the veggies cook. Then take the veggies off of the steam and serve.
If you're steaming asparagus, usually the problem is that the bottom stems are thick and tough, while the top heads are very soft and tender. There is in fact a special steaming pot for asparagus that is tall and skinny. That way you can sit the stems down at the bottom where they get super-steamed, while the heads stay far away from the steam and do not get over-cooked.