Basically, when you enter into an expantion system, you should sooner or later find these Military Strike zones and Security Operation zones as you would the high intensity/low intensity conflict zones. Just target it, sc to it and you're in. Kill things then return to one of your control systems and turn in the vouchers for merits.
Just remember that you may need to fly a good distance, like towards a particular station or planet before they might show up on your nav panel.
For instance, in the beta, we had to sc 17000ls from hyperdrive entry towards Isreal Station before we could see what was called the 'crime sweep' zones... which was just one of A. Duval's things.