When extending the network in our homes, we are faced with several challenges, as not many homes were pre-wired with Ethernet to every room. But most homes are pre-wired with Coax (RG6 typically) from a central point to multiple rooms throughout the home.
Coax supports high-bandwidth transmissions with low-loss and can be adapted to carry Ethernet with the right adapters. However, since coax is often in use by cable-TV or Satellite-TV we need to break down the options into multiple categories.

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Unused Coax segment

Even if some of the Coax segments are used for other services, there might be a segment going to an unused bedroom on the upper level, where you’d like to place an additional WiFi access point for better WiFi coverage on that floor. In which case, the deployment of Ethernet to Coax adapters on either end of that wire will deliver 100Mbps Ethernet to that room and you can plug in the Access point.
This $20 kit has all you need (get the one with the included power adapters).

Or spend a bit more (~$120 for 2 adapters) and get a full Gigabit across the coax using this kit from GoCoax.


Cable TV

Due to video and or Internet from the ISP being on the cable, you need to use the right type of Ethernet to coax adapters which are known as MoCA. There is Moca v1.1 (speeds up to 700Mbps) and Moca 2.0 (speeds of 1Gbps). Generally the v1.1 is good enough and possibly more stable.
Using 2 of these adapters will enable getting Ethernet onto existing coax, even if shared with Cable TV (note that you might need coax splitters if there is an existing TV/Set-top box connected to the coax in the target room).
The new MoCA 2.5 supports full gigabit, and when used with the right splitters and filters (read the reviews), can co-exist with current cable services. This GoCoax model seems to work well.

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Satellite TV

Most Satellite TV deployments in the past few years include bridging the home network onto the Coax used to feed the Digital Video Recorders (DVR) and Set Top Boxes (STB) at each TV. So this makes it easy to get a network feed back out onto Ethernet, as anywhere there is a DVR or STB, we can convert off the Coax.
Actually, if the DVR/STB has a network port on it, it could be as simple as just plugging in an Ethernet cable and connect that to a device that needs network access. So a DVR sitting next to smart TV can be directly connected to the network by running an Ethernet cable from the DVR’s Ethernet port to the Ethernet port on the TV and reconfiguring the TV to use wired networking.
If you need to connect more things, like a BluRay and a Roku, then just add a small Ethernet switch.

 If the STB (like the DirecTV Genie mini) does NOT have an Ethernet port, you can still get the network access by adding one DECA Ethernet to Coax adapter before the the Genie (note: you need splitters and short Coax segments as well as the adapter). You will not even need a power supply, as the Genie will supply power over the Coax. This makes the common scenario of a wall mounted flat panel TV with a Genie mini mounted behind simple to deal with, as all that’s needed is this adapter, and run the Ethernet into the TV. Keeps everything tidy and hidden behind the TV. 

Much more information, diagrams and options listed in this white paper over at Solid Signal

Example pulling Ethernet from Sat Coax to feed switch

Example pulling Ethernet from Sat Coax to feed switch