on linux. downloaded jar file from website. im not a java dev i dont know much about this
it seems jar files follow zip file structure
when i run java -jar <exec-name> it says Error: Could not find or load main class Main
how do i get around this and install the minecrfat mod?

so i just move the jar files into ./minecraft/mods ?

You don't run mod files. You install a mod loader to your launcher profile, and then you just place the mod jar files to the .minecraft/mods/ directory.

Personally I would recommend using the 3rd party open source PrismLauncher as it makes it easier to manage modded instances. But you can also just get the Fabric installer and run it, and it will create a new Fabric profile to the vanilla launcher.