Mint is the classic herb for shade, and it needs to be kept moist. It is a perennial plant and can become quite invasive, so it should always be grown in a container: one with a built-in water reservoir may give greatest success. It should be repotted every so often, dividing up the crowded root system. It can be quite prone to the horrid little flea beetle: a tiny, rounded insect that disfigures the foliage. I have grown mint inside a wooden cage covered with fine mesh to keep them out; another strategy is to frequently check for the presence of the beetles and flick them into a jar of soapy water to drown them!
There are around 25 species of mint. Perhaps the best for culinary use are Mentha spicata (spearmint) and Mentha x piperita (peppermint). Native river mint (Mentha australis, ht 30 cm, sometimes called wild mint) is a smaller, more delicate edible relative, and also grows well in damp, shaded spots.