I definitely think there is a correct way to put on makeup, but it also depends on the effect you are going for, your skin type and your age. The general order I would do (for natural looking makeup) is -
Moisturizer
Concealer (under eye, any blemishes or dark spots, side of your nose)
Light foundation or tinted moisturizer (to even out your skin tone - Laura Mercier has a great tinted moisturizer - if you are 16-25 you probably don't need this step)
Translucent Powder (something with no color to set your makeup - if you have dry skin forget the powder)
Blush (something that matches the color of your skin after you've worked out, or been in the cold - experimenting with creme blushes is great too and helps give a more natural glow - dab a little on the apples of your cheeks only)
Eye Shadow
Eye Liner (I like to use a brush and black powder - I wet the brush and dab a little under the top lashes where they meet your eyelid ridge - try not to get it on the ridge - it takes some practice, but looks great)
Curl Lashes (Optional)
Mascara
Lip liner (Optional)
Lip gloss or Lipstick
If you want to vamp it up a bit for going out you can do it in the eyes and/or lips - more liner, smokey eyes, etc. Trying to recreate looks you see in magazines is fun too.
Good Luck!