Normal goods are easy to understand. When income rises the demand curve for normal goods shifts out, or shifts up and to the right, because more of goods are demanded at every price. Inferior goods are a little less obvious, but are still fairly easy to understand. The term inferior good, in this context, has nothing to do with quality. What makes a good an inferior good is how consumers' demand for that good changes when their income changes. Inferior goods are those goods for which the demand curve shifts down, or back and to the left, when income rises and for which demand shifts out, or up and to the right, when income falls.
Inferior goods are simply those goods purchased in the place of more preferred, but more expensive, alternatives. Thus, as income falls demand for inferior goods rises as fewer of the more expensive preferred goods can be purchased, and as income rises more of the preferred goods can be afforded so demand for inferior goods falls. Some examples of goods that are usually inferior goods are: generic or "store" brands, discount clothing, fast food, matinee movies, and so on. It's important to keep in mind that what might be an inferior good for one person may not be for another, either because of differences in tastes or differences in income. For example, for someone whose income is very low, fast food like pizza, burgers and tacos may seem like a luxury, but for someone with a higher income these foods may be strictly inferior. No good is an inferior good at very low incomes. For consumption to fall as income rises, logically it must be the case that at lower incomes consumption was increasing with increases in income, otherwise the good would never have been purchased at all so it's consumption wouldn't be able to decrease.