I can think of a number of ways, it depends on your needs. Apple makes a thunderbolt to gigabit ethernet adapter, just plug it into the thunderbolt port and it works, no drivers or configuration needed. Apple also makes a USB adapter, have not checked recently but it used to be USB 2.0 and only did 100baseT. There are third party companies making USB 3.0 gigabit adapters, I have one of these. Kind of handy because it also serves as a USB hub. It requires a driver however, and I did have a couple crashes that could be related.
Then there are third party docks that plug into the thunderbolt port, they have a variety of other ports also, check the different manufacturers. These will be much more expensive and larger than the methods above.
[doublepost=1474645748][/doublepost]Just another thought, since you say you are doing this at home. What year is your MBA? From 2013 on, the MBA has had 802.11ac wifi that is very fast. The Blackmagic speed test reports about 60 MB/sec connecting to a shared disk on my LAN over wifi (I get about 100 MB/sec with ethernet). So unless you really need full gigabit speed, you might want to upgrade to a router that supports 802.11ac wifi and do everything wirelessly.