How to take decent photographs of eyes?

I'm working on my portrait photography and I can't get really clear pictures of people's eyes. I have a Nikon d60, I know it's not the best of cameras, but does anyone know the best settings and things to put this camera on for the best portraits?

Subject head should look in the direction of the light source.

In a household use the windows as light source, the bigger the better.

Ask the subject to look in the direction of the light source.

Focus on the eyes.

Use "aperture priority" to adjust manually the aperture, the camera will take care of the shutter speed for you.

Use the "shutter speed priority" to adjust manually the shutter speed, the camera wil take care of the aperture for you.

Avoid "auto" mode because in low light the camera will try to use the flash.

You may use a reflector to bounce back some light on your subject, it will help soften the shadow and will bring more light into the eyes (depending where you put it).

Reflector can be bought for $20 or you can use a mirror, white foam board, white cardboard, piece of wood with a white sheet around it, anything with a reflective surface can be use.

Silver = harsh light.
Gold = will give you a warmer light.

Then next you'll have to learn how to process the eyes with your software because eyes tend to look a bit grey and you'll need to fix that to make them pop. If you don't know how to do it just look on google, there are plenty of tutorials out there.