Failing surgery, there is not much one can do to get rid of eye bags, but there is however a quick method to disguise them using the simple technique of colour correcting and highlighting.
Using a natural shade of foundation cover face and under eye area, blend with a brush to give you a flawless finish. If you suffer from dark pigmentation or discolouration use a coral/orange tone to neutralise blue/dark brown. For purple/vein tone use a yellow to knock back the colour. Make sure to really blend this in well, a little at a time.
Then using a cream concealer one shade lighter, lightly dab around the under eye area with your ring finger, making sure to blend well. My last tip is to use a very fine brush and dab the light colour into the dark crease of the eye bag to highlight and make the skin seem even in colour.
Make sure you keep to JUST the crease.
Continue with your normal make up routine. Ideally, some eyeliner and mascara is all you need to enhance the eye area (and detract from the eye bags) only if you prefer not to use eyeshadows. Eh voila, your excess baggage has disappeared!