We use Respondus Lock Down Browser. It will not allow two browser screens open along with copy, paste or any other save functions. You can lock a quiz until it's finished without exiting. Nothing is a perfect solution against cheating but this helps a bunch. It also keeps them from saving the material in digital form. I know the arguments are they can use another device to look something up or just snap a picture of it. We use timed quizzes, only show one question at a time, shuffle questions and answers.
There is another feature in Moodle that you can use to help, and it's in the quiz set up where you can click a browser security setting that uses some java scripting to limit what they can do. There's also a tool called "Safe Exam Browser" that works with Moodle but I have not used it. I think it's come a long way in the last couple of years but when we started it wasn't suitable for our needs so we went with Respondus for a fee.