Yes, it can be planted in the fall. Asparagus is normally proprogated with root cuttings and/or clump division. This helps to ensure that you get what you bought. Order soon.

There is a lot written on proper planting procedures, but I go by the ones who say that asparagus will seek it's preferred depth which is about 4". It wants extremely rich soil in full sun, and please pull any weeds that work their way through the mulch. Remember that you will have to pick the new spears by hand in the spring, so don't make any bed wider than you can comfortably reach across without stepping on the bed. I recommend a good all-weather path around all edges of the bed (you'll be glad of it the first time you pick immediately after a spring rainstorm). Prepare the bed by incorporating a large quantity of rich organic material -you can use as much as 50% *composted* manure. The easiest way is to remove the soil to a depth of 8" and then layer compost with the soil until you have a slightly raised bed (it will sink overwinter). The usual planting directions have you planting in a 12" deep trench and gradually filling that up; don't bother. Instead, make the trench about 4" deep, plant the roots about a foot apart, and cover with 5" of mixed soil/compost. I'd recommend straw as a mulch, at least 6" deep. Next spring you can cut any spear that is fatter than your thumb (won't be many); the harvest increases considerably in following years as you can then harvest anything fatter than your little finger. Stop harvesting once there are more ferny leaves than stalks in the bed (that will be a 4 to 8-week harvest); let the plants make their leaves --don't trim back until they die in the fall. Do always keep a good mulch between the stems. Enjoy!