How to install Google Play services on an Android 6.0 emulator?
1) Go get GApps for the emulator from http://opengapps.org

2) Unzip to get


GmsCore.apk
GoogleServicesFramework.apk
GoogleLoginService.apk     
Phonesky.apk


Launch the emulator from the command line, on linux you do

./emulator [name] -no-boot-anim -writable-system


on windows it's probably 

emulator.exe [name] -no-boot-anim -writable-system


Make sure you have adb access to the emulator.

adb remount


last but not least, push everything to system.

adb push GmsCore.apk /system/priv-app/


(and repeat for all the other APKs)

then reboot with

adb shell stop


and

adb shell start