One of the easiest ways to incorporate games into teaching is to use Jeopardy. I have used it to liven up test reviews in courses as disparate as calculus and remedial arithmetic. Free templates for the game can be gotten by searching “PowerPoint Jeopardy Template.” You can then enter questions and answers into the template. There are also versions available that teachers have posted for various classes, with the questions and answers already written in.
To make game play more collaborative, and to ensure that everyone is working, the whole class can participate in finding the answer to each question, rather than just one student at a time, or the class can be split into teams. Student appreciate being able to go back over the game at home as further review, which can be facilitated by posting the game online, for example, in a course management system such as Blackboard.