RPi Zero has no built-in Ethernet, so it's possible that Raspbian has not recognized the external USB to Ethernet adapter (i.e. missing drivers) or that it goes in conflict with another device and your router can't assign an IP address.
My advise is to login to your router and look at DHCP leases table for a device named raspberrypi.
Of course, the easiest way is to connect a display to the RPi's HDMI port or if you have a USB to TTL Serial cable (i.e. Adafruit 954) you can examine the Console messages.
According to Raspberry site to enable SSH you need to put a blank file named "ssh" in the boot partition (on Windows you should see it as a separate drive i.e. "boot (E:)") of the SD card:
For headless setup, SSH can be enabled by placing a file named ssh, without any extension, onto the boot partition of the SD card from another computer. When the Pi boots, it looks for the ssh file. If it is found, SSH is enabled and the file is deleted. The content of the file does not matter; it could contain text, or nothing at all.
If you have loaded Raspbian onto a blank SD card, you will have two partitions. The first one, which is the smaller one, is the boot partition. Place the file into this one.
You need to connect the Ethernet cable to your router and then find the RPi's IP address (raspberrypi.local may not work). The easiest way is look at router's DHCP leases table.
