Interesting veg this - its actually a member of the Brassica family. I have never grown this before but bought it in a pot from a nursery. I was advised to keep it in a pot as it can run riot and can be extremely invasive(there are mixed views on this around the web - some say it can be happily companion planted with potatoes, some say it will take over).
I have been advised that a new plant can grow from even a small bit of root so beware when picking!
Info and history
The advice I have been given on harvesting is that you dig up the whole plant when its dormant in late autumn/winter and then use the large main root for cooking and use the largest of the offshoots as roots for next year. The root will survive for a few weeks in a sealed containter in your fridge until you want to use it.
Horseradish is also reported to have diuretic and digestive uses and be a natural antibiotic.
I look forward to trying out a couple of recipes later this year which I plan on sharing (assuming all goes well) - feel free to let me know if you have any good ones!