Actually, it's not all that hard. Even though there are hundreds of channels in those frequency bands, there are relatively few control channels. All you need to do is block the control channels and you prevent the phone from operating.
There is another technique that is somewhat more elegant -- spoofing the tower. Since cell phones will latch onto the strongest signal, you just need a signal that is slightly stronger than the towers in the area. That signal has enough of the correct protocol behind it that the phone uses it and doesn't connect to the real system.
This is a variation on the pico-cell concept that they are talking about for aircraft, subways, etc.