If your PC is connected via LAN not WIFI you can follow this procedure.
After setup you will be able to ping raspberrypi.local and use the IP address to SSH into your pi zero. You will need nothing more than a usb cable from pi zero to your computer.
Setting up Pi Zero OTG
The quick way (No USB keyboard, mouse, HDMI monitor needed)
For this method, alongside your Pi Zero, MicroUSB cable and MicroSD card, only an additional computer is required, which can be running Windows (with Bonjour, iTunes or Quicktime installed), Mac OS or Linux (with Avahi Daemon installed, for example Ubuntu has it built in).
- Flash Raspbian Jessie full or Raspbian Jessie Lite onto the SD card.
- Once Raspbian is flashed, open up the boot partition (in Windows Explorer, Finder etc) and add to the bottom of the config.txt file dtoverlay=dwc2 on a new line, then save the file.
- Finally, open up the cmdline.txt. Be careful with this file, it is very picky with its formatting! Each parameter is seperated by a single space (it does not use newlines). Insert modules-load=dwc2,g_ether after rootwait. To compare, an edited version of the cmdline.txt file at the time of writing, can be found here.
- That's it, eject the SD card from your computer, put it in your Raspberry Pi Zero and connect it via USB to your computer. It will take up to 90s to boot up (shorter on subsequent boots). It should then appear as a USB Ethernet device. You can SSH into it using raspberrypi.local as the address.