You can use the REST API by entering its URL in a browser window and entering your credentials.
If you want to use the REST API through a web browser, you can log on to the Rule Execution Server console and switch to the REST API by adding /api/resourceNameAndQuery to the Rule Execution Server console context root. The application server automatically handles the session and all you have to do is log on at the first call or at each session timeout.
For example: http://localhost:9080/res/api/ruleapps
http://host:port/res/api/resourceName/templateParameters?queryParameters
You can now write and call REST methods as described in Using the REST API test tool.