Basic Checkmate: King and Queen
This one, we will keep short and simple.
Idealy, "By the book", the King/Queen checkmate looks like this:
There is, however, one consideration to make. When using the King and Queen checkmate, it is important to allow your opponent's King a place to move, or stalemate will ensue. See the following diagram:
As we can see, it is Black and Black is not in check. Black has no where to move. White has blundered away an otherwise inevitable checkmate and must walk away from the table with an unnecessary stalemate.