Ginger
 

I just love ginger in my cooking, but wanted to try my hand at growing my own, and it is VERY easy:

• Purchase a piece of fresh ginger root at the grocery store.
• If you broke it off another piece, let the ends dry out for a few days.
• Plant it in ordinary potting soil, about an inch below the surface.
• Water it in and wait.

It will grow to become a lovely plant, putting up more and more growths as the time progresses.

In the photo below, the piece on the left is the original one I planted in June, and the one on the right is the new growth when I harvested it today, some 5 months later. Both pieces are usable in cooking!

http://firstrays.com/Pictures/ginger.jpg

Ginger is a favourite of mine too. You should try and grow galangal. It's very similar to Ginger - in use of root - but has a unique taste. It's used in many Thai recipes. It's 4x the price of Ginger. Lemon grass is another.
Unfortunately I'm not able to grow any of these but do grow many types of basil.

I've never even heard of galangal...

Good summary
What's the Difference Between Galangal and Ginger? | Kitchn

You can often find fresh galanga (Alpinia galanga) and turmeric (Curcuma longa) in Asian markets. They are easy to grow so long as you don't keep them too wet at first. Turmeric is a small plant, potentially a house plant. Galanga grows to 10 feet / 2.5m plus in a good climate. Take care the growth points haven't been cut off. Gingers are attractive to spider mites.