The Pi Zero has the limitation of only having a single USB port. If you want to put your Pi Zero on the LAN, then you need to add a network port, this is normally done using a USB Nic.

I hate buying anything for the Pi Zero that costs proportionally more than the Pi Zero, and USB network adapters fall in to that category. Pay a few quid for one, and you only get a crappy unreliable Nic that is sold as USB2, but is normally an old USB 1.x and that fails all the time, believe me, I have tried a lot of them.

Then I came across this website http://raspi.tv/2015/ethernet-on-pi-zero-how-to-put-an-ethernet-port-on-your-pi

What they have done is used a network module that runs on the SPI bus. Its a cheap unit that you can get from ebay for around £3, and while they are cheap, they are reliable, albeit a little slow, but not so slow that they are unusable. I will take reliability over speed any day.

Here is the unit I purchased from eBay for £2.07p

The seller on eBay is chips-fans and while it has the same part number as the one used on raspi.tv, the pins are different, which is a bit annoying, but it wasn't to hard to work out.