The first thing I do is apply a non-creasing primer like Too Faced Shadow Insurance or Urban Decay Primer Potion. A small amount tapped on the area will help adhesion, prevent slippage and creasing. You want to avoid products here that are too thick and dry because they will crease and even sort of create fine lines and you'll be ridding one problem while creating another. Liquid concealers are often too thin however. My favorite is the Laura Mercier Secret Concealer duo which provides a salmon toned concealer that will counteract the blueness of the area, and a brightening shade that you apply after. After I do my eye makeup I like to apply the Laura Mercier with my finger (it takes some warming up to get creamy) by honestly rather crudely patting on the salmon side, then the brightening side. I apply my foundation all over using a dampened Beauty Blender that has been squeezed into a towel and then as a last step I use the excess to go over undereye are. The excess on the sponge goes over the concealer nicely, blending it all into a uniform shade.
Other products to try would be Maybelline Age Eraser in Brightening (salmon tone) which is great because it is a twist up sponge applicator that is fast, but it isn't extremely full coverage if you have particularly bad undereye circles, it does however work for most. Tarte Colored Clay CC Concealer is also fantastic and creamy, a perfect consistency for undereye and great coverage, as is MAC Pro Longwear Concealer which comes in a convenient little pump.
The key is to concentrate the product where you're darkest, and keep it minimal where you crease. In terms of setting, I wait a minute until the concealer settles into the crease under the eyes, take my beauty blender and remove the tiniest bit while smoothing the area, then immediately powder. I use matte or satin finish shadow for powdering under the eye and a section of the (damp but not at all wet) Beauty Blender and I press the powder on. I use a shade lighter and brighter than the rest of the face especially since powder can create a darkening effect when placed on top of creams and liquids. Pressing will really sink it into the product as opposed to dusting the powder on top. Do all of this in daylight to make sure it looks right and to get an idea of how much product is needed and that colors are working for you. Drugstore alternatives: Hard Candy Glamoflauge, the Cover Girl concealer that looks like lipstick, Sonia Kashuk concealer palette, LA Girl Pro Concealer