The best way is to hook up your system, there are a few way to hook up an old system to a new TV.
https://atariage.com/howto/connect.html
You may have to scan for analogue channels.
If you get just a black screen on a game, try another til you get a picture, the black screen game may just need to be cleaned.
https://atariage.com/howto/clean_cartridges.html
It appears you want to determine that they work to sell them. list as "untested" and let the market determine the value (these games are pretty robust and probably still work)