Remove Earth's atmosphere
Noting that the OP specified effective rather than efficient ways, kill all the messengers. It's the only way to be sure.
Let us have a look at some of the ways to communicate over distance (not an exhaustive list):
- Line of sight electromagnetic (EM) signals
- Satellite-bounced EM signals
- Landline signals
- Atmosphere-bounced EM signals
- Ground station-relayed EM signals
- Ground wave vibrations
Lots of the above are vulnerable to artificially created EMP or the natural equivalent, although not in the way you might think for satellites. (High altitude EMPs are designed to affect equipment over a wide area on the ground below through atmospheric interactions, it does not affect satellites themselves as much.) However, as this xkcd question examined, the bandwidth of a courier carrying a shoebox full of memory sticks is massive, albeit with very high ping times.
So the short answer is - you can attempt to disable all of the terminal equipment, jam the signals, cut the landlines etc, but unless you can also prevent the couriers taking the message through manually there is no way to prevent the mail getting through.