Such tests will ask you questions about how you normally behave, what you like doing, what type of person you are. You may be asked to rate yourself on various statements, or say how much a certain description is like you. Sometimes you have to say which of a set of descriptions is most like you, and choose one which is least like you. Sometimes the questions relate to a work situation, others are more general. These tests usually don't have a time limit. They can be done using pencil and paper, or completed on computer.
Other personality tests may require you to tell a story based on a picture. or to describe what an inkblot looks like to you. These tests require special training and they may only be used by psychologists who have done the necessary training.