How do you re-hydrate horseradish root?

For Drying Seed.

Either dry on the bush or pick when ripe. Either way, harvest the whole seedhead or strip individual seeds and dry under cover for a week or so depending on the weather.
You could hang the entire plant up or just the seed heads. Store in an airtight container.

For Drying Leaves.

Harvest the entire plant ( or however many leaves you want) and hang to dry in an airy place. This won't work in humid weather. Don't bunch too many together or the air won't circulate well. When the leaves are crisp strip them and store in airtight containers.
Another method is to oven dry them although this is a bit more tricky. Place on baking paper on a wire rack in an oven set on low - 90 degrees F or so with the door open. Watch carefully. Remove when dry ( hopefully before they're burnt as well!) and store as above.