Asparagus is a great vegetable to grow for a garden, especially because it is a perennial (so it will come back year after year).  Patience is key with this one, because it takes a couple years to get asparagus going.  You don't want to start harvesting the spears until the plant is 3 years old.  Although you can start asparagus from seed, it is easier to start with 1 year old crowns that you can purchase at the nursery.

In warmer areas, you can plant crowns in the spring or fall (just make sure it is 4 or more weeks before the first frost in the fall).  For colder areas, stick with spring planting after the last danger of a hard freeze in your area.  Choose a well drained area with full sun exposure, and with a soil pH above 6.  Start by digging a trench foot deep and 10 inches wide (the length will depend on the number of plants, but you will want to space the crowns a foot apart).  Back-fill just under half the depth with compost, manure, or peat.   Place the crowns on the mound you created and spread out the roots.  Cover the crowns leaving about an inch of soil above, but make sure the soil line is just below the trench.  As the shoots emerge, gradually keep adding soil until the trench is filled back in.  Make sure that the keep the asparagus well hydrated as the spears emerge.

During the first year, you will want to let the shoots grow without cutting them.  The shoots will look fern like when they mature.  They will die back in the fall, but just leave them be.  In the spring of the second year in, cut and clear out the old fern like growths (remove any mulch at this time if you used any also).  Apply a little 10-10-10 fertilizer (about a capful for every 3 feet of your original trench, now row).  You can mulch them in if you wish, and keep the area weeded.  However, you don't want to harvest anything this year either.  Again, let the spears be and die back.  The spring next spring, you will follow the same steps as the year before, clearing the old growth, etc.  This year, you can harvest.

When the stalks are 6 to 8 inches (or are about as think as your finger), they are ready for harvest.  Let skinnier shoots go, and grow to their fern like stems.  When you harvest, cut the spears just below the soil line.  The crop will increase with each passing year, and you will be able to harvest for about 6 weeks.  After that time, let the remaining shoots go and grow fernlike.  Continue the maintanence as before each spring.