Open your image up in Photoshop, or whatever program you decide to use. I decided to use a picture of my little cousin that I took this summer (I MISS YOU CRAZY BERMUDIANS SO MUCH, BY THE WAY. JUST SAYING.). Hahaha. :)
Create a duplicate of your background layer. If you are very, very new to photoshop you do that by right clicking on your background layer then clicking duplicate layer.
Use the lasso tool to select both eyes. Draw a circle around one, then shift+click to select the other one at the same time. Then go to Select > Refine Edge. Smooth it out until you get a nice circle, and then feather it as much as you want. I tend to do mine around 7 or 8.
Next, go to Filter > Sharpen > Unsharp Mask. Try to keep it under 100 or else your eyes will look ridiculous. Remember, you don't to overdo them.... which I am more than guilty of doing... you just want to make them pop.
Then go to Image > Adjustments > Brightness/Contrast and adjust it to your liking. Deselect the eyes (CTRL+D) and use your eraser to erase around the eye.
There really isn't a wrong or right way to do it. It really varies between picture to picture how I adjust everything, so really just do anything to your liking. :)
And here is the image completely edited just for the heck of it.