Hardy to Zone 3
Asparagus roots can be planted as soon as your soil can be worked. If you must keep them for a short period, wrap them immediately in slightly damp sphagnum moss. If you do not have sphagnum moss you can wrap the roots in wet paper towel, put in a bag and store in the fridge. You must keep the roots moist. Choose an area of your garden that drains well. Start by digging in a generous amount of compost, then dig a trench 10" deep. Form mounds of soil at the bottom of the trench about 12" apart. Set each crown on top of a mound and drape the roots over the mound, like a wig over a head. This enables the roots to establish themselves faster, as they will get even moisture and nutrients. The crowns should be at least 2-3" below the soil surface. Fill in the trench and support with more soil as the stalks begin to grow.
Asparagus needs to send energy to the roots during the first couple of years, so don't harvest any spears until the third year. Mulch heavily each year around the spears after they come up to prevent weeds and hold in moisture. Let the tops (ferns) grow and do not prune in the fall. Each spring, cut the old ferns that have died over the winter, pull off the mulch and add more fertilizer or compost. Mulch again when plants have emerged. Harvest thicker spears when 6-8" tall on third and subsequent years. Carefully cut with a knife at soil level.