Shredded fresh turmeric root makes a much tastier tisane than any sort of dried turmeric powder. It smells not unlike an infusion of the familiar powder but has a much richer and somewhat carrot-like favor, some pepperiness, and a sweetness that emerges faster and more intensely than when turmeric powder is steeped.
I steep the shreds of one medium-sized root (c. 12 g) in a large (c. 900 cc) teapotful of just-boiled water, and find it quite palatable after 20 minutes. No milk or sweeteners are needed (these feature in South Asian preparations of haldi chai as a treatment for colds).
Beware of staining your hands, clothes, and everything in your kitchen yellow. (Staining your soul with turmeric is acceptable, however.) To get rid of stains on kitchen equipment I use Soft Scrub, a harsh cleanser that contains bleach, grit, and a number of other substances. That will quickly remove the sticky yellow stains from countertops, plates, and blades. Wash everything thoroughly after you're finished with Soft Scrub, to get rid of its own residues. (The ingredients are currently listed at http://www.softscrub.com/Soft-Scrub-With-Beach-Cleanser .) Soft Scrub reacts with the turmeric to produce a dark red/brown color, and you may at first imagine you've cut yourself.
I don't know how to get the yellow stains off my fingers, so I use inexpensive rubber gloves to hold the turmeric root while I'm shredding it.
Fresh turmeric apparently has anti-fungal properties, and the fresh roots do not quickly go bad if kept in the refrigerator in a sealed plastic bag and a paper towel to absorb moisture. If an infusion made from the fresh root is left out overnight. it is totally without cloudiness the next morning. (The same is true of rooibos tea.)
The Chinese name for turmeric root is yùjīn 鬱金 lit. 'verdant gold'.
I posted more on fresh turmeric tea here.