Under-eye creams can be too heavy for the season. Why not try a gel formula instead? Take your pick, ladies!
I will suggest you to use under eye cream by Mamaearth to remove dark circles. This cream is natural and effective.
You need to apply an eyecream before you apply and moisturizer and be very gentle on your eyes as the skin near your eyes is very gentle and thin.
Also, I suggest you watch some eyecare videos on YouTube to get a better idea on how to apply an eyecream. I suggest watching Beauty Within or Mixed Makeup videos.
If you're just starting out, I suggest you use the Biotique's Seaweed Eye Gel.