An ethernet cable [ RJ45 ] is the blue or yellow cable that you use to connect your computer to the router.
In this case you would use it to connect from your extender to your computer.
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The extender would need to be plugged into a socket in the "Shed".
Some are wireless AND cable compatible.
I think you would get a better connection using the cable, however, you could try it wireless and see what it is like if this is more convenient.
My wireless connection is always 5 bars.