In the morning, you still need to cleanse your face even if you haven't had anything on your face overnight. Your body heels overnight and therefore it expells toxins out of the skin which will be on the surface and they need to be cleaned away. You should also use eye cream in the morning as well as at night time to keep them hydrated. To protect your skin throughout the day, apply an antioxidant cream and sunscreen. The importance of applying sunscreen on exposed areas (evening in winter) is very high, as UV rays are the main cause of aging and of course, skin cancer. Then, lastly a moisturiser which suits your skin type but remember to let the sunscreen dry before applying the moisturiser as if they are applied together than the SPF is cut in half and not as protective.
At night, you should cleanse your face twice. First time to cleanse off the make up on your face and secondly to cleanse any purities off your face. Apply your eye cream and if you are at an age when you should be using an anti aging cream (it's best to start at 25 in Australian climate, 35 elsewhere) apply that. Follow by a night cream or your normal moisturiser, the choice is up to each individual.
Another important part of skin care is to exfoliate regularly, and to use a mask. You should exfoliate twice a week (try the middle and the end) and then apply a mask once a week after you exfoliate (at the end of the week).
Also, if you can afford (sadly, not everyone can) try to have a monthly facial just for maintance. The machinery they use in a facial works better than cleansing your face yourself. Often Student Day Spas are cheaper than a normal Day Spa. The cost of a basic facial can be from $30 to $150 depending on the products used in a facial and what you have done. I would also recommend going to a salon to find out which products suit your skin type and find out how to suit any skin conditions you have (weak skin, acne, pigmentation, etc)