I have dark circles and puffy undereyes. I got Laura Geller Concealer in a tiny makeup compact. I use my finger to blend it. I find it is better than a brush. I try not to put too much on because it looks worse. I only use the concealer on the dark part of the circle. Pat Pat Pat and blend it in. It doesn't cover 100% but I don't think anything covers 100%.
Also, if I had money I would get plastic surgery and do my eyelid and under the eye, the bags.