While SharQ's node on this contains some very good advice, it also betrays a lack of professional training on the topic, so I hope he doesn't mind me adding a slightly different view.
First so far as defining winning, surviving is definitely the way to go. If you are a kamikaze type, and consider it a win if you die but take your opponent with you, my advice will be of only marginal use to you. I am also assuming that by knife fight we mean that your opponent has a knife as well.
So far as how to hold the knife, there are basically three positions, like an axe, like a sabre, and like an icepick. Holding it like an axe is likely to be the default position for most people, as it's most likely the way you hold a knife when doing other things. This is what SharQ called "tip forward edge down". It is not the best way to hold a knife for fighting, but obviously it can work.
The sabre grip is usually the choice of the trained fighter. In this grip you hold the top of the handle, where the blade comes out, between thumb and forefinger, with the rest of the fingers curled loosely around the rest of the handle. This grip gives up some strength but gains quickness. This will normally be your best bet.
The icepick grip involves holding the knife reversed from the axe grip, with your thumb locked over the butt of the weapon. The edge should usually face outward from your forearm, although sometimes it is appropriate to reverse that, particularly before a downward thrust which is likely to be blocked. The icepick grip can be deadly when used right - it allows for quick defensive slashing blocks as well very strong stabbing thrusts. However, it sacrifices range which is detrimental to our goal of surviving. If you use this grip you need to be very aggressive, and this increases the risk to your own life, as well as to your opponent.
So, assuming you have chosen the sabre grip as I recommended, now you want to assume a flexible stance with your feet about shoulder-width apart, knees bent, and only a slight crouch. Stay away from close quarters and don't allow yourself to be cornered. Fight defensively, wait for your opponent to commit an attack, then circle back and away from it, slicing out as you do so, aiming usually for his wrist, or anything else in range in a pinch. The object of this strategy is simply to stay alive and cause your opponent to bleed. If you can do this for a few minutes, he'll eventually lose enough blood that he will begin to experience asphyxiation. Eventually, if all goes well, the opponent collapses, and it's time to call for medics.
Caveats - this will only work if you have some room to maneuver. If hostilities begin at short range and in a corner, this tactic stands no chance at all. In that case you're probably better off with icepick grip, an aggressive thrust and an attempt to capture the opponents weapon with your off-hand. This will not work if you opponent has very good footwork or you have very poor, or both. It relies on outmaneuvering the attacker consistently. It helps to have a longer blade than the opponent, and having a significantly shorter blade will make this more difficult. With all those caveats, however, it is still probably your best bet to get out of a knife fight alive in most situations.
Running from a knife is a very good idea if you can get away with it. However, be very careful, being literally stabbed in the back is a very predictable consequence of running either too soon or too late from a knife-wielding tough. So it's appropriate to consider other options, even in the worst scenario (he has a knife and you don't) because you may have no other choice than to fight it out for a time until you get a good opportunity to run.
If facing a knife unarmed, you really are in a bad situation, and no amount of good advice will make up for that. You should definately run at the first opportunity. But if you have to fight in this situation, remember to always block with the back of your forearms and hands, not the front. The skin is thicker there, and your precious veins not so close to the surface, so getting cut there is not quite as bad as on the inside. If you mix it up you are going to get cut - count on it. You are going to bleed. Count on that too. You must end the fight, either by a succesful attack or a good flee, in a relatively short time - before your blood loss critically weakens you. If you think you can wrestle for the knife succesfully go for it. Holding the knife immobile while striking the soft parts can be a winning strategy here. Don't hesitate to use the nutter, particularly if both of your hands are tied up. And if you can knock him on his ass for a moment you've gained a great opportunity to run for it.