One of the most important elements to get right in portrait photography is the eyes. The eyes help tell the story, and should be the first thing that the viewer is drawn to. Although you can of course have a portrait where you don't have eye contact (or don't even see the eyes for that matter) it should be because of a deliberate choice. In order to get your portraits to stand out, you need to emphasis the eyes - and this article should give you some tips to achieve this.
1) Focus on the Eye
You want to make sure that the eyes are in perfect focus - those viewing a photo will forgive a lot of sins if the eyes are sharp. This is a lot harder to do if your subject is moving about, so trying to get your child to sit in one place long enough for you to take photos is incredibly helpful. You can use the camera's central focus point and use the focus recompose method (To focus recompose, press the shutter halfway to lock focus, and still with your finger halfway on the shutter, move the camera to the composition you want) Focus on the eye closest to the central focal point. Alternatively, and important if you are dealing with a shallow depth of field, is to manually toggle your focal points so that you choose the one that hovers over the eye. This saves you from having to move the camera after focus has been set, which can throw off the focus.
2) Use the Rule of Thirds
Using the rule of thirds to frame your photograph will draw attention to the eyes and give them more emphasis. You can do this in camera or later in post processing. (If you are unsure about how to use the rule of thirds, you can read this article here) Try to have an eye in one of the intersections, and/or both eyes along one of the lines.
3) Give the subject space to look into
If your subject is not looking at the lens - try to leave a little room in the direction they are looking in. This helps draw the viewers eye into negative space, rather than be cut off abruptly at the edge of the frame.
4) Find The Light
Another great tip for getting the eyes to "pop" is to use natural light to your advantage. This is usually referred to as catchlights - literally where the light catches the eyes and makes them sparkle. If you have an older child you can ask them to move around in a circle until you can see the light hitting their eyes. Of course with a younger child you will have no such co-operation, instead scout out the light ahead of time - I've used my husband before to gauge where the light is best, then brought in the child! This is usually facing into the light source (or angled to it) for example a window, open doorway, or toward the direction of light outside. If it is sunny, don't have them look into the light (it will make them squint) have them face away from the light and use a reflector bounce light back into the eyes.
5) Mind Your Settings
To get great eyes in portraiture you need proper exposure, good use of light and sharp focus. Make sure your shutter speed is high enough (a common culprit of soft focus), and that you have a wide enough aperture to get both eyes in focus (assuming that is what you are going for). Also try to keep your ISO down especially if you are using a cropped frame camera - high ISO's can result in a lot of noise, which is OK, but you won't get such a crisp image as you would at low ISO's. I try to take most of my portrait style shots outdoors - I get great options for directional light, and enough overall light to keep my ISO down and my shutter speed high. Only problem is it gives my son even more room to run from me!
Other Posts You Might Like:
Using the Rule of Thirds in Child Photography
How To Photograph Children: Natural Light
Nailing Focus Part 2: Focus Techniques