The secret ingredient for moist banana bread is sour cream, according to About.com. This website recommends mixing the sour cream with the moist ingredients before adding the dry ingredients to the bowl.
Banana bread is a quick bread, so it is important to avoid overmixing, which creates gluten and makes the bread tough. To ensure the bread remains moist, begin checking the bread after 55 minutes in the oven. Cooking is complete when the top develops a crack and a butter knife, inserted in the center of the bread, comes out clean. Cooking the loaf longer dries out the moisture from the bread.