As others have said, a knockout is typically not the result of a blow to the nose, but to the chin.
The brain is basically a loose spongy thing trapped inside your skull. When you receive a hard blow to the head, the brain will hit the inside of your skull – much like when you shake a nut, and you can hear it rattles against the shell. This will temporarilly shut down the brain, causing a trauma otherwise known as a "knockout".
When you hit the front of the face, the head is moving rapidly in one direction. When you hit the jaw from an angle, the head is not only moving backwards, but it also rotates, thus making the brain more likely to bounce against the inside of your skull harder or more times – thus making the trauma more likely or severe.
To answer your question, there are several ways a fighter can prevent this. The most predominant precaution, is to train the neck muscles. The stronger the neck, the harder blows you can sustain. Fighters will also warm up the neck muscles before a fight.
Secondly, it is all about practicing for head blows, getting hit a few times in a controlled environment, and know how to handle it. If you are constantly sparring or doing drills with head blows, you are more likely to react. Ideally you would block, parry or evade, but the last method of defense is to "brace for impact".
- Tuck your chin down. Assuming you keep your guard up and close, this makes it easier to protect the vulnerable chin and nose. A strike to the top of your skull will probably not harm you (much). It also means that the top of the spine (neck bones?) will absorb the blow better, since it will be hit at an angle, and your head is less likely to move back (I hope this makes sense).
- Tense your jaw. Your jaw is vulnerable – lots of small bones, and not very strong muscles to support a blow. By biting down, your jaw will not be able to move independently of the rest of your head, so will hopefully not be dislocated or broken.
- Tense your neck. This is a crucial step. It makes sure your head is not moving too rapidly, thus rattling your sponge.
That said, a well placed kick or strike to the tip of the jaw is baically like hitting an off-switch. It doesn't even have to be very powerful, it just requires a light tap. I've been on the delivering end of it a few times, and I am always surprised as to how little is actually nescesarry for a knockout. Ironically, it has never been my intention to knock people out with the technique, it has always been intended as a setup for the REAL knockout technique.
Likely effects of a hit to the nose, is a broken nose. the nose is basically cartilage (not bones), so it's fairly easy to crush. It will bleed profusely, and in some cases you will not be able to continue the fight, if they cannot stop or control the bleeding. You might suffer cosmetic injuries, but for the most part a broken nose is an easy fix.
Likely effect of a good hit on the chin, is immediate knockout. If the brain trauma is severe, you might suffer from light or severe memory loss. The jaw might dislocate or break, and you might loose some teeth in the process (even if using a mouth guard). Cosmetic injuries might happen, and you might need surgery which may or may not be invasive, and may or may not have a long term effect. Some organizations may bar you from sparring or fighting for a temporary period.
Fortunatelly, at most tournaments where full contact techniques to the face is allowed, the fighters are also well prepared with years of practice. They know how to prevent getting hit, and they probably already have several fights under their belt under a bit softer ruleset. They know the risk – and often have to sign documents that states exactly this.