Pick a relatively clean background without distractions. Vegetation, solid walls, and water often make good backgrounds.
Make sure your subject is at least 10 to 15 feet away from the background. This will also help give a clean background.
Make sure you focus on the subject's eyes and that there is light in the subject's eyes.
Avoid the phrase, "1, 2, 3 smile." Just talk to your subject in a natural way and tell them they look great or "that looks perfect" as you instruct him or her on how to pose. If you want your subject's attention just say, "Look over here at me. Tilt your chin up just a bit. You look great!" Snap away. Most people will smile naturally. If they don't smile say things like, "Give me a bigger smile." Or "You have a nice smile." Is they're still not smiling just say, "Give me a smile." Never count and then ask for a smile.
Choose a medium length telephoto lens such as a 100 mm lens or zoom lens with the focal length set between 100 and 200 mm. Set the f-stop to 4.0 if the lens allows you to do that. The combination of a medium telephoto lens and a 4.0 f-stop will limit the depth of field (the range of focus in the photo) and will help minimize the background, but it's also good to have a non-distracting background to begin with (point 1). This type of lens also minimizes distortion.