Spring, as soon as the ground can be worked is the best time of bare root hostas. For nursery plants, wait until the last frost date for your area has passed. here is some general info on hosta planting and care.
Yes, if you can dig in the ground, you can plant it. The sooner the better, Hostas are very hardy, early-bloomers but you may not get flowers this first year. If they are white, be sure to smell them, white Hostas can have a wonderful scent. Can you see the eyes where the foliage will sprout? Those should be at the top when you bury it, an inch under should do well.
If it's muddy, don't pack the soil too tight around it, some small air pockets will help it transition from dormancy without rotting. Rain and the action of the newly forming roots, and worms if you have them, will even things out soon. A few inches of leaves on top after you get it planted would make it feel right at home, mostly around the edges of where you've dug. When you see foliage sprouting, move the leaves away from the foliage a few inches.
Growing it won't be a problem since hostas are relatively pest-free. Slugs are the most common pest which work at night leaving small holes in the leaves. Slugs require moist and dark conditions and prefer soft, immature leaf growth. However good horticultural practices can also reduce slug damage.
All great advice above, I would just add, Hosta's like shade or part shade, dont let them dry out too often, and when the clump gets too big, dig it up, chop it up and replant, too big is normally after about 5-6 years, Come autumn, I like to throw a top dressing / mulch about 2-3 inches thick for winter protection, all year round, look out for slug / snail damage and find your own way of treating this or your lovely leaves will be shreaded.
Best of luck. WeeNel.