Sorry for asking a simple question.

So let me get this right they note the speed, check the chart for who's in the area then have a cigarette then phone and have a discussion who's going to attempt to shoot the missle down.

The Russians have a control module which tracks and decides what missle is going to intercept. There was one captured in March in Ukraine.

Is there a main control module or is it human input?

If they're used in Nato they have the facility to communicate. That being said how does the command decide what unit fires first if the incoming missle is within range of a few systems.