There are five basic types of root systems: fibrous roots, long tap roots, rhizomes, roots with "eyes", and fleshy tuberous roots.
Fibrous Roots (example: Tall Hybrid Phlox)...Dig a hole twice as wide and twice as deep as the bare roots. Carefully spread the roots out in the hole. Holding the roots with one hand, suspend them in the planting hole at the proper depth. Fill in and around the roots with soil until the hole is completely filled. Tamp the soil with your hand to remove air pockets. Create a "saucer" around the planting hole with soil, mark the planting, and fill the sauce with water. Let is soak in and fill the saucer again until the roots are completely watered.
Long Tap Root (examples: Hollyhocks). Follow the procedure outlined above for Fibrous Roots.
Rhizomes (example: Bearded Iris)...Dig a shallow hole 2-4" deep and twice as wide as the rhizome. Create a small mound in the middle of this shallow planting hole. Place the rhizome on top of this mound and spread the roots on both sides of the mound. Fill the hole with soil, but only partially cover the rhizome. Water thoroughly.
Roots with "Eyes" (example: Peonies) ...Dig a hole twice as wide and twice as deep as the root. Holding the root, with "eyes" pointing up, at the proper planting depth, fill in and around the root with soil until the planting hole is filled. Firm the soil with both hands and water thoroughly. (Note: It's important not to plant Peonies over 2" below the soil surface for proper blooming.)
Fleshy Roots (examples: Daylilies, Hosta) ...Dig a hole twice as wide and twice as deep as the bare roots. Create a mound in the planting hole to hold the roots and the crown (where roots meet the stem) at ground level. Spread the roots over the mound. Fill the planting hole with soil and firm with both hands. Water thoroughly.