It’s likely that you haven’t configured that you want to build a .JAR/Artifact.
If you go to to your Project Settings by doing:
Ctrl+Shift+Alt+S
and click on the Artifacts tab on the side.
Then click the Green + at the top, you’ll be able to configure your project to build an artifact.
Then Build > Build Artifacts... should not be greyed out and your should be able to build your JAR.