Harvesting roots seems much more daunting than snipping blooms off of a plant. Yet with a little know-how and proper tools, you can enjoy your own homegrown medicine directly from the earth.
At a glance, here is the flow for processing roots herbs Dig-up > Shake loose dirt > Wash and Scrub > Chop > Dry
Using a hand tool with a long thin blade is ideal. I actually purchase the tools made to weed out dandelions for harvesting purposes.
Using my hand tool, I like to dig a hole along one side of the root and loosen the soil on this side. I convert to using my hands at this point and feel around the root and loosen the soil on the remaining sides. Once I can have a firm grasp, I start moving the root in circles around the hole to loosen it before pulling out. Shake off to leave as much dirt as possible in the ground.
I use a potato scrub brush to wash and clean roots in my kitchen sink. I cut them into smaller pieces for drying. Depending on the root, I may use a knife, kitchen shears or my clippers.
You can simply leave them out to dry is a cool, dark place. However, your dehydrator if you'd will dry them more quickly. Check your settings, but it will take roughly 6+ hours at the temperature of 120 degrees. Roots harden when dried so test to see if they feel firm before storing.
Things go much more smoothly if root herbs are planted with loose, aerated soil (in deep beds if you grow in raised beds) so really the first step to easier harvesting is to choose the proper location to grow them. It's also best to pick a spot where they can remain as-is for a few years as most take that long to mature. Keep this in mind next spring!
A general rule is to harvest spring roots before the plant flowers and fall roots after the plant has gone to seed and the seeds have natured, but before frost.
Here is a cheat sheet for planting and harvesting your root herbs.