Portrait photography is no easy stuff and learning photography involves a number of intricate techniques. Just pointing a camera at someone isn't generally going to get you quality photos. So remember to:

Take lots of photos – As we cannot gurantee that every photo we capture to be perfect it is a better idea to capture a series of photos as digital photography is cheaper. An important rule of portrait composition is to show the empty space facing the person. For formal pictures you need a border so you need to keep space around people, or their heads. As most portraits aren't formal there is no need for a border.
Pick the Correct Lens – The 105mm lens is an ideal one for single person portraits. The longer focal lengths are better for isolating subjects, and used at large apertures (like f2.8) give a pleasant out of focus background without being too heavy. For larger shots, shorter lengths are helpful (70mm). Great care should also be taken while focusing and you really need the eyes to be in focus.
Setup the Environment for the Shot – The better shots are more often made than captured – set your self up in the right place with the right gear and the correct setting and then take lots of photos.