Normal Skin: If you have skin that is normally smooth and healthy looking then you have 'normal' skin. The main products for you to avoid are those that will dry your skin out, or conversely cause it to become oily. Products labelled as 'mild' or 'light' will be ideal.
Dry Skin: Dry skin may feel tight after washing and can irritate easily. It may be especially noticeable in the cold or the wind. Tips to look after dry skin include keeping hot showers short (or using cooler water), limit cleansing to morning and night using a creamy cleanser, and use a good moisturiser. The key word for those with dry skin is HYDRATION.
Oily Skin: Oily skin is generally characterised by shininess, and a tendency towards larger pores and perhaps blemishes and blackheads. Facial scrubs to avoid clogged pores and then an oil control moisturiser are the order of the day.
Combination Skin: As the name suggests combination skin combines 2 of the skin types above. It generally refers to a skin type whereby there is a defined 'T-Zone' around the nose and forehead and chin area that is oilier than the rest of the skin. The best way to care for this type of (very common) skin, is to use either specialist products for combination skin, or to treat both types of skin with different products.