Q:

Google play api references not recognized

I'm following https://github.com/playgameservices/android-basic-samples
And I can't get the project buttonclicker2000 to compile. 
See the screenshot below. 

A:

All the import statements in grey must be added to your project libraries. 
At the link you provided, https://github.com/playgameservices/android-basic-samples, go into the scripts folder, then into the eclipse_aux folder.  Download the .jar file within and save it somewhere you can find. 
Now in Android Studio, in the left project tree, right click on "ButtonClicker" > New > Module
Then select the Import .JAR/.AAR Package option. 
You can click the "browse" [...] on the far right and locate your jar.  
Sync the project: right click app > Sync app
You should be golden after that.  Alt-Shift over RED methods/code relevant to your added library and you should now be able to quick import.