I had this same problem last year. Unfortunately I haven't found a way to effectively conceal dark circles if the skin under the eyes is already too dry (otherwise the concealer/foundation flakes and it looks awful). So you have to moisturize first.
I'd suggest finding an eye cream that is specifically designed for moisturizing (as opposed to anti-aging or fine lines). I've found Philosophy's Hope in a Jar to be excellent for this. You could also try a moisturizer designed to combat dark circles such as Benefit's EyeCon.
To fight the redness I'd suggest Prescriptives Redness Relief gel. I've been using it on my cheeks, which tend to get red all year round, and it has definitely helped reduce the ruddiness.
Once you have the dryness under control, try Laura Mercier's secret camoflauge concealer and apply with a concealer brush. I just read (can't remember where - perhaps InStyle) the secret is to apply the concealer just below the darkness (not directly on top) because that's where the shadows are.
Anyway, these are just the tips that have worked for me. Hope this helps or gets you started on the right path!!
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"Beauty is in the eye of the beholder and it may be necessary from time to time to give a misinformed beholder a black eye."
Miss Piggy
I have been using Bliss all-around eye cream for quite some time and i really like it. I use it in the morning under concealer and feel it works really well. If you have a sephora near you, they will probably give/make you a sample.