What you want is a wireless bridge. If you search online for the best wireless ethernet bridges you will get a fair number of results and some decent articles to read about.
ie:
https://www.tomsguide.com/us/best-wifi-extenders,review-2225.html
So, a wireless bridge is just like the name sounds like. You are bridging your wireless connection from the basement to another wireless device. This second device acts as a repeater and booster. So, it can go on the main floor, or wherever you need a boost to the signal. Sometimes you may need two or three of them to get a decent signal everywhere in your home.
It provides wired outputs as well, so you can plug in hard wired devices directly to the repeater and it will connect to your home network.
You have to configure the devices as the instructions will direct you. But, once connected you don't need to touch them again.
Typically they will mirror your home wireless settings so the SSID and password will be the same throughout your home. You will connect your wireless devices to them just like you do at any location.
Just a question... If you have the router in the basement, what is connected to your cable box? Why not put the router there instead of in the basement?