Sometimes you have to improvise with a class I device that is encased in plastic Usually have to try finding an exposed screw, though even then they may just be screwed into plastic - some VAX hoovers are like this. In this case I open up the cover to expose the earth connection and test continuity from the terminal. Are you sure this is a class I appliance, or is it class II?
PAT testing is a series of tests, and those tests are slightly different depending on the class and type of equipment. I know most people think PAT testing is pretty mickey mouse, but it does require competence. Remember - when you PAT test, you are taking on responsibility for the assessment of electrical safety. Insurance is a must. My advice to you is get properly trained - do a course. And make sure it is a C&G2377 course.
PS there is a sub-forum on here for PAT testing - look in the forum for Inspecting, Testing & Certification