Jamming (active):
Broadcast so much noise at the relevant frequencies that it drowns out any other signal the devices might try to interact with. You throw a lot of power into going LALALALALALALALA at the frequency bands you expect the devices you want to jam to be interacting at, then they can't hear each other over you. It's actually not a particularly hard engineering problem until you start worrying about heat and efficiency - you just build a transmitter and broadcast noise at high power.
Blocking (passive):
Use a Faraday cage or sheer mass to prevent signals from being broadcast into or out of an enclosed area. Mass attenuates signals depending on thickness, density, and frequency. A Faraday cage uses a powered metal mesh to maintain constant voltage at a surface, which can kill most transmissions without the need to turn your building into a bunker.
But assuming this is actually allowed by your local laws, you still shouldn't do it. It's hazardous and unethical since it will also disrupt e.g. emergency communications. If you're bothered by impolite cell phone use, you should pursue a social remedy which allows for extreme cases where manners are not the biggest concern, rather than a technical one which is blind to significant edge cases.
For military applications:
You don't have an enclosed area to work with, so you mostly use jamming devices with as much power as you can manage. But this gets used less than you might think from Hollywood, since a major cost of using them is that you're very loudly shouting your general position to anyone who cares about that and access to some basic electronics. Also the really good ones are set up as buildings or vehicles, it's not going to be small if you want power on the order of "shout so loud a civilian radio station can't hear itself think."
Passive compliments:
Anti-radar stealth technology, which is where you try to make yourself as much of a pain in the ass to make out clearly as you can manage. This is far more difficult since you don't have a controlled environment to play with, but there's still a lot you can do with clever shapes and surface design. Also the point is less to make yourself invisible, than it is to reduce the amount of advance warning that an opponent would get, or their ability to respond to changes in your vector.
Chaff countermeasures are easier, you basically launch a bunch of stuff that's highly reflective at the frequencies people are trying to track you with. I think this is mostly an air-to-air thing. It actually works pretty well, at least in terms of "make it less likely that you get shot down." But if the other guy has reasonably modern targeting systems, you can bet he's got chaff too since it amounts to a thing that shoots out tinfoil confetti.
Otherwise I think you just broadcast noise on the frequency your device is trying to use.