Extracting flavor of ginger in cooking
For extracting (to water / ghee / oil), the best way I've found is to slice long slivers of ginger paper thin, as thin as you can. The extra surface area provides better saturation, and being extra thin promotes optimal extraction. Remove the ginger after 10 or so minutes, or once you pick up a strong smell of it. 

For flavoring where you leave it in, I like to use a micro plane and grate it very finely, while being careful not to burn it. It does get bitter if overcooked or burned so timing and temperature are important. That might be the slightly acrid / pungent taste you're picking up.

In soups and stuff, I generally just follow the recipe the first few times and then adjust if I feel like I could use less ginger to get the same result. A few slivers can give the same taste as a 1cm square chunk.