Since there is no OTA option for the Android releases of KOReader, the easiest way is to download the .apk file from one of the sites and "sideload" it onto your device. I download the current nightly from
http://build.koreader.rocks/download/nightly/ and use the "Save as" to shorten the file name to something manageable. Then I just transfer it from my PC onto my Android device, via USB, and open it there where I an offered the option to install it.
You might want to find a closer site, there are a number listed in the OTA settings.
Luck;
Ken