You can upload photos to your album:
https://www.bikeforums.net/g/user/550203
Steel-Chromium-Molybdenum alloy (chromoly)
You just need a "shifter", but there are a number of different varieties depending on the bike style and bike age.
If the bike dates back to the 1980's, then you might need a "downtube shifter" or "stem shifter" or "bar end shifter" depending on the location and handlebar type.
Newer bikes can have brake-shifters (brifters), or "thumb shifters" (thumbies). Perhaps "grip shifters".
In most cases the shifters will only fit one side, so right/left, or pair is important.
Most modern shifter cables are in two types, Shimano, and Campagnolo compatible. They have small barrel type cable ends, with the Campagnolo branded ones slightly smaller. A few vintage cables will be different.
I tend to choose the cheapest STAINLESS STEEL cables I can find.
You may also need "cable housing".
You can often find cable sets at your favorite department store. Often double ended, so save the end you want, and discard the other end.