Well, basically, good SA would dictate that one does not enter a furball situation at all in the first place. A furball is like a kettle of soup where frozen sausages are dumped in. No matter where the sausage maneuvers to, in the end, it will have to cook sooner or later
However, if one does decide to commit himself to the kettle...
Typically, a furball is a low-alt, low-speed situation where many fighters are engaged in a tight area. The first thing you should consider is if the numbers on both sides are matched. One or two friendlies trapped inside five~six enemies is not a furball. It's a barrel where the fish inside are about to be shot.
The next thing to be considered is the types of planes flying around. If there are enemy planes like 109s or P-51s up high, and the Spits and N1Ks are down low, it is very unlikely the energy-senstive fighters will follow you down into the furball. Those fighters will only engage when you attempt to get out of the furball. Usually the planes flying at low level are typically good turning, but low speed fighters. You can jump in, pull some high E-bleeding maneuvers and still get out, since they are slow. However, at that point the vultures circling at high alt will engage.
Thus, the next thing to be considered is the "rythm" of the furball. The speed of fighter reinforcements/people who were shot down previously re-upping and arriving at the scene again. According to this speed you have to time your attacks and escapes. You should think of getting out of the furball when the dar indicates the next batch of enemy reinforcements are within 1 minute away from the scene. Look around for friendlies arriving at the scene, and as they are about to arrive, get out of the furball.
The next thing one should consider is the tactical sense inside the furball.
Do not chase an enemy plane if there are more than two friendlies on it. When many friendlies chase one target, when the enemy reinforcements are otw, warn them about it. If the guys flying around you are smart, some of them will drop off and grab alt for the next engagement. If they're dumb, ignore them and grab alt yourself. You warned them, they didn't listen. No need sacrificing yourself for people who willingly invite disaster onto themselves.
When you meet a situation where someone looks like in need of help, make your judgement calls. If there is a P-51 surrounded by three Spitfires, and you in a 109, you cannot help him. If there is a La-7 chasing a 190D-9 and you are in a SpitV, you cannot help him. If there is a Spitfire chased by other Spitfires and you also in a Spitfire, you can help him. Or, if there is a La-7 chased by a Typhoon and you are in a something like Yak-9U, you might be able to help him. Some people are in situations beyond of help, others are not. Learn the difference between those two.
If one side has won the furball, the furball arena slowly moves on nearer to the enemy field. The reinforcements will come slower for the winning side, and quicker for the losing side. This is what keeps furballs alive long. Always feel the "force" of the two sides flowing around two airfields. Ride with the force and you shall live, ride against the force and you shall be shot down.
So there, that's all I have to say