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IntelliJ does not recognize the folder your class files are in as java sources. Right click on the "src" folder then "Mark directory as" and finally sources root.
Then IntelliJ should treat them as classes and build your project. Then either open the class containing your main-method and press the green play button next to the main method to run it.
Alternatively, you can right click on the class and then click "Run ${Application}.main().
And finally this should also enable you to setup a run configuration as described in your original question by now finding the GUIDemo class as main class.
Note that project SDK needs to be setup as described in @Loading...'s answer.
Hope that helps and enjoy IntelliJ.
Just to make note, this project seems to be using older build technology called ant. I am not sure if this has any impact on Intellij as I have not used ant with CE version.
I am wondering if you have setup your Project SDK correctly within Intellij.
If you can open up your Project Structure window (shown below), you should see your Project SDK defined.
My hope is that you do not have an SDK defined and that is why your icons are the orange j instead of the usual blue C. If it is not defined this should hopefully allow things to fall into place and for Intellij to recognize your main class (assuming CE version has ant support which I am not sure).
When you're in a java file that contains a public static final void main(String[] arg) method you can press Ctrl+Shift+F10 to make and run a temporary run configuration for the current class. This can save a bit of time when setting up the configurations.
Alternatively you can try to share the .idea directory with him, as it contains all of the project's settings. I'm not sure what other options will be shared though.
it's easy, Your friend must do this and this setting is changed in the "Default Project Structure..." dialog. Navigate to "File" -> "Other Settings" -> "Default Project Structure...".
Next, modify the "Project language level" setting to your desired language level.
IntelliJ IDEA 12 had this setting in "Template Project Structure..." instead of "Default Project Structure..."