Eyes

Eyes are an extremely important element of any portrait. You can have a perfect composition, beautiful colors, and an amazing model, but if you get the eyes wrong, your photograph will suffer.
When shooting a portrait, the best thing to focus on are the eyes. It doesn't matter if the hair is a little less sharp and it's ok if the arm is a bit out of focus. What's not ok is if the eyes are blurry. There are very few occasions when you may want the eyes to be out of focus. For the majority of the time, you will want eyes that are a sharp as possible.
Sometimes using auto-focus makes this task very difficult. It will focus on the hair or the nose, or just about anything but the eyes. Even the eye lashes can drag the focus away from the detail of the eyes if your depth of field is shallow enough to let it. So don't be afraid to switch of the auto-focus and go manual.
When you've got your eyes sharp and in focus, there are still other ways to make them pop. You can use color matching: have your  model wear an outfit that accents or matches their eyes. Or shoot with elements in the photo that the same colors as your model's eyes.
You can also make the color pop in post. If you have Photoshop, try creating a layer mask that only effects the eyes. Bring up the contrast and saturation a bit. Be careful with the saturation, though. You want to keep the original color of the eyes. (Unless you actually are trying to change the color.)