We put a 2-3" piece of fresh root (available at almost ANY grocery store, even here in the sticks of rural Iowa) in a blender with the olive oil, 'blenderize it' and strain that through a mesh sieve.
Even easier would be to 'rough chop' the ginger into chunks, put in a bowl with the olive oil and 'smoosh out the ginger juice' with the back of a spoon...and let it sit overnight (or for a day or two).
Yet easier than that? Take a 3-4" piece of the root, smash it with a hammer really good and throw it in a tea kettle with a cup or two of water...bring it to 'a whistle' (boil), and then let it steep awhile. Add the sweetener (or not) of your choice, and wallah, fresh ginger tea.
Also (just fyi) I keep about a pound of chopped ginger in a glass container with several cups of organic expeller/cold pressed peanut oil. So whenever I want yummy stir-fried rice/sprouts/veggies, I just put a few tablespoons in the wok with a couple of crushed cloves of garlic, heat it to sizzling, throw in "goodies"...and instant Chinese Stir-Fry by the plateful. FANtastic...and oh so easy :)
(I've been gonna do the same with some Bariani Olive-Oil & fresh garlic cloves. Then I'd have therapeutic garlic oil...that's good for anything & everything...AND I'd have the perfect base for virtually ANYTHING Italian!)