I would start by introduce my students to the site . The idea used in Real English site is to show how English is used in real life situation, so I will show them an example of real life aspect where English is used each week . I will play a video in the class and then we start commenting on the video and play it again and again when needed .
After that I would ask them to make a small play and start acting like the people on the video using the same expressions that were used in the video .
For example : today's lesson is about greeting people. I will play them a corresponding Real English video for the function. Then we start playing roles together and great each others . students will take turns so each of them will play all the roles and use different aspects of language .
As a homework, I will ask my students to go over the exercise the site provides for the video that I have already show them earlier in class, which are made with free software and called "Hot Potatoes".For example: I can design an exercise where the students have to type an answer, but if they are wrong x times, then the same exercise transforms itself into an easier multiple choice exercise! In this way, the student is challenged but never lost. All he has to do is keep on trying until he gets feedback about his/her answer.
We (my students and I ) can also join Real English on Facebook page where questions about the videos or lessons are often asked, as well as questions about English in general. I will answer some of these questions myself , to help and encourage my students to do participate and so they will feel that they are interacting more than learning and that will make them more motivated to use their" real English ".
This way, with the use of Real English website my students will watch and listen to real people, so they will be more ready to speak English as it is in the real world than other students who are learning the old way. Because as we all know, no one speaks " classroom English" .