Before putting on makeup, make sure that your face had been cleansed, and moisturized. I recommend the Cetaphil or Neutrogena brand for oil-free moisturizers.
Don't use any makeup products that are not, non-comedogenic, or oil-free since these kind of products will or most likely break you out even more.
Now, use an oil-free primer, i recommend makeup forever primers or hourglass primers. If you're looking for something affordable, Revlon's primer and L'oreal haven't broke me out.
So try that. I would definitely recommend using sponge (beautyblender) for a flawless finish. Try gradually layering foundation slowly, and don't put too much in one go. You'll definitely end up with a cake face.
First put on a thin layer of foundation or bb cream.
These are my recommendations:
Foundation: Revlon Colorstay, Bourjois Healthy Mix, Maybelline Fit Me
BB Cream: TheFaceShop water bb cream, EtudeHouse Bright Fit, Garnier BB cream
Then cover up your problem spots with concealer. (Makeup Forever Full Cover concealer, HArd Candy concealer, Bobby Brown concealer)
IF you don't have any concealer, double up your foundation to a concealer.
But remember; build it up gradually.
Have FUN! ^^