Are you in the Tree View? If so, look for an X in the upper right hand of the rectangle that each person has. Hit X to delete that person's profile.
If there are children or a spouse, you have to first delete each one of them that has an X before you can delete the "anchor" person. And X will show up on that person once they have no more dependents.
In Profile View versus Tree View, there is a pull down called ACTIONS in the upper righthand of the Profile and one of the actions is Delete I believe.