To learn more about OpenShift without needing to install it yourself you can use the interactive learning portal for OpenShift. This provides a set of guided exercises that you can work through to learn about using OpenShift to deploy applications.
To try out OpenShift running on the leading cloud providers you can use the test drive lab environments. These environments allow you to test deploying your own applications, or experiment with administering an OpenShift cluster.
Both the interactive learning portal and test drive lab environments are time limited. For a more permanent environment in which you can experiment with OpenShift, you can sign up for the free starter tier of OpenShift Online.