I'll take a crack at this one...
Obviously it will depend on the comparative airplane performance, along with the other available options. In this case lets assume similar performance, and a lack of other viable options to avoid death.
Scissors is all about decelleration. You want to slow down faster than the other guy, yet avoid his guns as he closes on you. Generally, simply cutting throttle to slow down won't get you out of his cone of fire, so that option is out. Instead, we can use some form of scissors to try to sucker the attacker into overshooting your flight path. This is a sucker move... and by that I mean it only works if the attacking pilot fails to counter effectively. If the attacking pilot is paying attention and takes basic steps to avoid the overshoot... you are likely doomed.
So I'm in this situation for example... I'm in my Jug (P-47-D25) with a bandit on my 6... say an FW-190 A5... a very similar plane to the one I'm flying in most way... a close fight. He is closing moderately and I am flying at about 250 Mph at low altitude. I can't out-turn him, too low to dive to escape, and no friendlies in the area. He has more E, so I can't zoom to safety or use vertical moves and expect to win. Ruh roh. I'm in bad trouble, and I'm going to be forced to risk a sucker move to force an overshoot, or at least to force him to break off long enough that I might gain enough separation to escape.
So, given that setup... scissors of some sort are a viable option. Give my E state and low altitude, in this case I choose the flat scissors. Now, my job here is to increase the closure rate by flying a longer flight path than my attacker. I'm going to start with a fairly gentle break slightly high and lets say to the left... at this point he should be at pretty long range... D 1.0k or so on my FE and closing. My goal is to get him aggressive by giving him a look at a nice big fat target in an easy deflection shot. I want him concentrating on lining up the shot, not the closure rate.
If you are entering the scissors (as the guy being attacked) you may want to cut throttle until you get down to your best corner/roll speed and to help increase closure. You will need lots of E to hit these hard breaks though, so don't slow down too much, once you are at the top of your best flying speed, open the throttle and WEP it, your hard breaks will burn more speed than you can generate. Next comes the hard part... I have to roll back the opposite way fast and pull hard, and I have to do it after he has committed to follow me, but before he guns my butt out of the sky. In a perfect world, I would roll under and pull hard back the other way just as he fires on the space where I used to be. In reality, you want to err on the side of caution and break before he has a shot at you. Just before. I'm flying this looking out my rear view BTW, watching his closure, range, and Angle Off Tail (AOT). Don't try to visually see him pulling lead before you break. Although that would work in real life, in an online game network lag means he can be pulling lead for a shot on his FE, and you don't see it. Only experience and deaths will tell you where that spot is, and it will vary with connection latency.
Ok, so I've made one break to the left, he sets me up for a shot, then before he fires I roll hard left (rolling under, using gravity to assist me) using stick and hard rudder until I am banked back to the right, the opposite direction. You hit that roll as crisp and fast as you can, and once you are on your new flight path you pull hard. Watch out your rear view again and you will hopefully see the enemy roll back to follow you. Wait until he has rolled onto your new flight path again, and started pulling for a shot, then hit your next roll again, fast and hard to reverse direction again just before he can fire at you. Now he is going to try and line you up for a snapshot... shoot you as you pull past him going the other way. Try not to cross his nose flying completely level, a bit low and below is nose will make it harder for him to nail you. Rolling underneath helps this, you can come out of it a bit nose low and start your pull, then roll up a bit more if needed so you don't hit the ground.
Ideally, after a couple of these, the enemy will overshoot your flight path. At that point you will either have a shot at him as he crosses your nose in the scissors, or you can simply roll onto his 6 and try for a shot. He may try to zoom away vertically, but if he has bled enough of his energy advantage trying to follow your scissors, you may be able to go up behind him and stay there long enough to gun his brains out. Beware though, if you try that without enough energy, you are being rope-a-doped and he will flip over and kill you as you stall.
Now for the nasty part. A wary pilot will see what you are doing and can easily counter it in one of several ways. The most common counter you will see is that the enemy will break off and zoom up above you. In this case he is conserving his energy advantage and letting you blow your E by executing hard break turns. When the enemy pulls off this way, you need to relax your turn and accellerate to gain E, watching him line up his next attach, and the game starts again. Planes that are better E fighters than the one you are in will generally choose this option.
Another counter is that the enemy pilot will use lag pursuit. That is, he knows you are trying to make him overshoot, so he will aim his plane behind yours through the maneuvers. In this way he doesn't get a shot in, but he avoids flying a shorter path... avoiding the overshoot. After a few scissors back and forth, you will likely be very low on energy, and the attacker will be able to camp out on your six and gun you down. Planes that are better turners, and have better low-speed control and performance will likely choose this option as a counter, as they can camp out on your six without worrying that you will simply out-turn them in a flat turn.
A most effective counter to the scissors is called a lag displacement roll. Essentially it is simply flying lag pursuit to avoid the overshoot, however instead of simply aiming behind the enemy, the attacker using lag displacement rolls will add a vertical component to his flight path, and then roll over into lag pursuit behind the prey. This is most difficult to describe, but it is most effective. Essentially if I am the attacker and you break left, then right to start a scissors, I would start a shallow climb then as you passed beneath me I would roll the opposite way and pull gently to roll around your flight path and end up back on your six, but taking a longer route to get there. In the end I maintian my position at your six, minimize closure, and also retain more E than the fellow pulling flat turns for a scissors. Planes that roll well such as the FW and the P-47 will often use this tactic to counter a scissors. If you see your enemy doing this... you are very likely about to die, as he is a very smart and dangerous enemy. This is not an intuitive move, so the guy on your six pulling these off is a very good pilot and his is not likely to get sucked into overshooting. Try your best, but prepare to die.
There is another move that is not really a counter but that you will see. When you start a scissors after the second break some guys will realize they are being suckered and will simply disengage. You break left, then right, and left again. The attacker follows the first two, then simply doesn't follow your third break, instead either running away level, diving away, or maybe a gentle zoom. In this case you have just gotten a bunch of separation that you can use to extend. You can then climb and look to re-attack on more favourable terms, or escape the situation.
Whew. Well have a read and fire away with the questions. This is a very complex subject so don't expect to "get it" all right away. Book some time with myself or another trainer and we'll work the scissors from both view points and it will really illustrate a lot of the points I've made above.