Implement a switch or if-statements in the OnUserInput method. Depending on the current value of screen, execute a specific code block. If screen == Screen.Screen1, then execute the code block and set screen = Screen.Screen2. When the player types something, screen == Screen.Screen2 would be true.
If you find this too confusing, complete the Terminal Hacker section because everything you need is already in the final game. You will just have to use the techniques you learnt to implement your own idea.