Hi JohnnyW,
To set role permissions at the screen level first go to Customize>Tabs. Click on Edit Tab Links... next to the tab that the screen is located in. From here you will given a list of the tab links (screens) within that tab and the option to set the role permissions for them.
Note that if the screen is on two or more tabs, you would have to run the same process for each tab. Also, if the screen is being called elsewhere by a pop up action then the user could possibly get access to it.
- Jason