Other than the basic skin care routine, you do not need to do anything extra or out of the ordinary.
OILY SKIN
Other than the basic skin care routine, you should use oil-free and alcohol-free facial products, especially an oil-free moisturizer. You do not want to use products with harse ingredients that will over dry your face and make your problems worse. You should use a shaving gel since it is made specifically for oily skin. A daily skin care routine is very important (do not skip days) since your skin collects dirt easier.
DRY SKIN
Other than the basic skin care routine, you should use very gentle products. You should use a moisturizer with an SPF protection since your skin is more prone to fine lines and wrinkles. Most importanly, drink plenty of water for hydration and MOISTURIZE, MOISTURIZE, MOISTURIZE (twice daily-do not skip this step!).
COMBINATION SKIN
Other than the basic skin care routine, you should use specific skin products for each area (oily skin products on T-zone and dry skin products on cheeks and eye areas). Definetely do not skip your daily skin care routine because your skin is all over the place and needs all the help it can get!
SENSITIVE SKIN
Other than the basic skin care routine, you should use alcohol-free products (this is very important). Use a moisturizer with SPF protection as your skin burns easily. Use a shaving gel instead of a shave cream. Do not use soap ever. Always do a patch test of any new products to see your skin's reaction. Do not use cheap products as they are made cheaply and will irritate your skin even more and cause more problems.