This is a reasonable question, and to an outside the simple answer of We don't / can't might seem a little bit jarring.
After-all, we live in a time of hacking, terrorism and so on and I can certainly see how this looks like a simple vector to create some havoc.
So, what's to stop somebody from setting themselves up with a Radio Transmitter and deciding to be Air Traffic Control for the day? Absolutely nothing. In fact, lower power handheld air-band transceivers can be purchased legally and cheaply by anyone. I have one near me - I could literally turn it on now and declare myself [Local Airport Tower]
However - the thing about Airband radio is that it's wonderful in its simplicity. At its core is AM radio which is basically unchanged since the early 1900's. This means a few things:
- The strongest signal doesn't simply "win". Multiple medium strength signals will simply merge into a garbled mess. This means you don't simply get to "take over" ATC's transmissions - all you can do is ruin them.
- Similiar to the above, there's no way (from outside) to stop the ATC signal. All you can do is stomp all over it - something which is totally noticeable.
- Even if you do "win over" air traffic control for some aircraft, communications is a two way process, and airband radio is simplex. This means only one person can speak at a time - at some point ATC are going to key in.
Pilots aren't automatons. We listen and build up a picture, we learn normal procedures and can hear stress in somebodies voice. We also know who we were speaking to. Combined with a decent situational awareness, we don't just do things without thinking - you can't just pipe up on the radio and ask an aircraft to fly into the ground.
And even if you did, and they initially believe you, real ATC is going to hear your readback and ask what the hell is going on.
By way of analogy, imagine you've snuck in on a conference call between an employee and a boss. And you start trying to speak on behalf of the boss - it's going to last all of 1 second before somebody realises something is going on. I think people tend to think of ATC as somewhat robotic, but it's still a human interaction and any good pilot will understand why they're being given instructions.
To attempt to interfere in Air Traffic Control in a way that is believable by the pilots is going to be incredibly difficult. You won't be able to use normal phraseology and cadence if you're attempting to step on real ATC, and that will concern the pilot. To do that for more than a few seconds and to to cause some kind of conflict with multiple aircraft is verging on the impossible.
The most likely outcome is more a denial of service, rather than some kind of spoof. It's not really a great vector to cause any damage. A nuisance, certainly and absolutely dangerous (and there's a reason it's very illegal!) but there are well established procedures for disruption in communications.
I've focused primarily on somebody trying to be ATC here, which is the way in which somebody on the ground would likely go about trying to make a mess. As for pretending to be a plane - firstly there are more technical difficulties because you'll be transmitting Ground -> Ground. I live within 2 miles of my local airport and often struggle to receive their transmissions when I'm at home.
Pretending to be a real plane that currently exists in the sky poses the same problems as above and any facility with RADAR is going to know something isn't right. Again, it might cause some initial confusion but you're unlikely to persuade somebody of something.
You could, in theory, pretend to be a light aircraft with no (or a faulty) transponder but really to what end? I guess you could cause a little disruption before somebody realises you're having a laugh but we're more into the realm of 'pranks' (Not that it's funny) now rather than serious risk.