How do they remote control the military drones?
Try checking out http://www.diydrones.com/ it may answer a lot of your questions.

As for multi-km links RF waves travel at the speed of light which is 299,792,458 meters per second that's more than fast enough for realtime control. The problem with long distance links is that for a frequency high enough to support realtime high-quality video such as microwave frequencies are line of sight for the most part. 

In order to get past free space attenuation you'll also need some power over FCC legal limits I'd assume, but you can get past that by getting an amateur radio license. There are ways around this, directional antennas but thats a whole story by itself.
(I am not a lawyer, I am however an Amateur Radio Operator)

Free space attenuation of signals (path loss) can be calculated as follows: Lfs = 32.45 + 20 log d + 20 log f

Where

Lfs = Free space loss in dB

d = distance in km

f = frequency in Mhz

Hope this helps!