Well, that's nice you are going to start a skincare routine! As you probably know, everyone has different skin and therefore need a different routine and different products for their skin.
1.) When you wake up, you should probably wash your face! Cetaphil Gentle Skin Cleaner is my recommended face wash. It's really gentle and helps prevent acne and stuff. You should also probably wash your face before you sleep! A lot of bacteria and other things accumulate on your skin during the day, so your skin will thank you.
2.) Moisturize! I think everyone has been told to moisturize at some point in their life. Like Emma said, Olay SPF 15 is good because it moisturizes well and also has an Sun Protection Factor (SPF) of 15. Remember that protecting your skin from the sun is very important to preventing skin cancer and also important for looking youthful and radiant as you age.
3. ) Exfoliation - Once or twice a week you probably want to use an exfoliant on your skin before you wash your face. Shaving exfoliates your skin, so that is good for you, and so is using a brown sugar, honey, and lemon juice face scrub. Or...
http://www.amazon.com/Queen-Helene-Masque-Mint-Julep/dp/B00008CMOQ/ref=sr_1_1?ie=UTF8&s=beauty&qid=1304950025&sr=1-1 < Queen Helen Mint Julep Masque! I love this stuff, but it can sting a teensy bit. Very good exfoliant and you can buy it at walgreens.
4.) Concealer - If you have any blemishes on your face (so pretty much if you are a human being) then you would most likely want to cover those! A concealer is super useful for covering acne or other little things on your face that you want to conceal.
http://www.avon.com/1/1/16510-mark-save-the-anti-acne-concealer-stick.html < Very good concealer, even if you don't have acne. It's creamy and goes on easily and is easy to carry around in your pocket or purse for quick touch-ups.
Foundation - Some people use foundation. Just like concealer it's not necessary, but I find that it makes me prettier, and who doesn't want that? Foundation evens out your skin tone and normally goes on over concealer and moisturizer. You'll probably want a light foundation that doesn't make your skin feel weighed down and make you feel hot.
http://www.pamperedprincesscosmetics.com/ < I LOVE her foundation. You can ever order a try-it size for $1.50 and it'll probably last you forever.
Extra stuffs - You should probably buy some makeup brushes for foundation/concealer, etc. ELF makes a really good overall face brush and you can buy it at target. It's only $1 and applies foundation/blush very well.
http://www.eyeslipsface.com/elf/brushes/brushes_and_applicators/total_face_brush