Google didn't publish Android 6 upgrade for Nexus 4 in the beginning of October 2015. My bad. However, only a week later the first AOSP-version* of Android 6 showed up! You can download all files needed here: http://forum.xda-developers.com/nexus-4/development/rom-6-0-android-marshmallow-pure-aosp-t3220900.
Instructions say TWRP 2.8.7 (recovery tool) is needed. My version was older 2.8.6. There is TWRP Manager (root) in Play store. Thus it's easy to download and install the latest version of TWRP on your phone. See here: https://play.google.com/store/apps/details?id=com.jmz.soft.twrpmanager. I guess Nexus 4 needs to be rooted in order to make TWRP Manager work. You have to find out how to root Nexus 4 for yourself.
Android 6 and Google apps
I downloaded aosp_mako-ota-eng.franzd.zip (= Android 6) and gapps-mm-fix.zip (= Google apps). Using a file manager app it was easy see where inside my Nexus 4 those two zips were. TWRP manager was able to flash both zip-files (first Android 6 and after that Google apps). No help from PC was needed. No USB cables. Nexus 4 only.
It took some time before Android 6 showed up. First there was no carrier. After reboot I was able to make phone calls. So now I have Android 6 up and running! Look at the pic below.
*AOSP = Android Open Source Project (= Google leaded project for Android)
My Nexus 4 running
AOSP version of Android 6