To color correct something you need to know what complementary colors are. Complementary colors are colors that are opposite of each other on the color wheel (yellow - purple for example). Layering one complementary color over another nullifies that color. So say we have under eye circles that have a purple hue to them, the correct color to correct them with would be yellow.
The reason why I explain this is because before I do anything I start by color correcting the skin using green, orange and yellow. Use a very light hand, you are trying to lightly correct any imperfections not audition for Shrek. I use Shu uemura pro concealer for this.
Okay so now you have corrected the coloring, we use foundation. I am of the belief that foundation should match your skin tone and never be lighter nor darker than it. Match the color to the skin in the neck and not the face to avoid any obvious lines. You can use fingers, brushes and sponges to apply foundation. I use a combination of all three.
My preferred foundation is actually a tinted moisturizer by becca cosmetics called luminous skin colour.
I will first apply a thin layer all over the face. Starting in the middle and blending outward. I will apply up to 3 layers of foundation to areas that need it.
Once the foundation is done I will apply concealer to areas like under the eyes and anything that needs a little extra cover and I finish with a very light dusting of loose powder.