I just read on another post how to do this. It's currently on the 7th page. "Growing Grocery Store Ginger".

There were two different methods listed. One seemed simple enough- basically plant it very shallowly and leave part of the root exposed. The other involved papertowels, baggies and fishtanks- not quite a strange as it sounds. Check it out and good luck.

Fresh is best! be sure ginger is firm without waxy substance. Use good soil blend, plant shallow in container
and do not over-water. You should see green sprouts with-in a few weeks or so.Be patient again,as with any plant--
do not over-water!! good luck!

When the soil and weather here was fully warmed, I put a large piece of ginger in the ground and it's growing fine. Unfortunately, this one isn't ground hardy here, though I'm going to leave it in, just to see....

It's easily replaced!

Robert.