As a beginner, I encountered errors every few minutes and this 'simple' missing script error can be a 'nightmare' for many others too.
Reason-
Most likely you are in the wrong directory of your terminal app and the error is somewhat like in the image given below.
Solution-
Go to the folder of the app which you are trying to run.
- To traverse up, use-
cd ..
To traverse down, use "cd (name of the folder)"
E.g- On my laptop, "my-app" folder was in a folder named "project".
After you have reached the folder then you can use "npm start" command and it should start without errors.