Disclaimer: I'm not responsible for anything. You can kill yourself with the circuits shown here.
transformers (or line output transformers) are high frequency ferrite-cored
transformers, used to generate high voltage needed to operate a Cathode-Ray Tube
(CRT) device (such as TV, monitor...). This voltage can be anything from few kV
to few tens of kV (color TV ~25kV; B/W TV ~15kV usually). Operating frequency is
around 16kHz in TVs, but the flyback can be operated anywhere from several kHz
to several tens of kHz.
In order to get some output from the flyback transformer you need a fairly powerful high frequency driver circuit. I'll give you a few examples of such circuits.
Types of flyback transformers
Type  is the older AC unrectified type. This
one isn't usually good for anything over 30kV, because it will flash over soon (and
also because it has usually low number of turns on its secondary winding and
thus it is difficult to get high voltages out of it). However it is often
suitable for higher power outputs than the other types. Found in old TVs.
Type  is probably the best one. Its secondary winding is divided into sections, which are separated by diodes, so there's just little AC voltage present, which makes insulating it easier, so it can output much more voltage than type  (voltages of 60kV and more are often possible). Found in newer TVs.
Type is the same as  except it has high voltage capacitor on its output, which makes it nearly useless for drawing arcs (because instead of an arc, you get a series of (loud) spark discharges). Found mostly in computer monitors.
Finding the high voltage negative pin on your
Before you can make any sparks with your flyback, you must find the high voltage negative pin. If you have the old type flyback without diode, it's easy. You can find it with an ohmmeter, the secondary winding will have anywhere from few tens to few thousands ohms.
If you have the new potted type with build-in diodes, it can't be measured with an ohmmeter, because the diodes starts conducting at ~20V. For this purpose, connect a positive voltage of about 30V (three 9V's in series) to the flyback output wire, and measure a voltage between negative output of the power supply and all pins on the flyback's base. The pin that gives the most voltage will be your negative output, which you should in all cases connect to the mains ground.
Now some circuits for driving your flyback transformer:
Circuit 1: Single-ended driver
Output power: Medium to low
Output voltage: High
This circuit works best with the newer type potted "diode-split" flybacks. It can provide quite high output voltage (50kV from diode-split transformer is not unusual). This driver is not too efficient above around 100W at which the switching transistor starts getting very hot. If you want higher output power I suggest the second driver.
The switching transistor (IRFP250) needs a small heat-sink. Wind a primary windong of 12 turns of insulated wire around the exposed part of the ferrite core.
Turn the "duty cycle" pot down, and set the "frequency" pot to greatest resistance (lowest frequency). Turn up the duty cycle until you can just hear a high-frequency sound. Make some sparks with the flyback (they will be quite small at this point) so you know the driver is working.
If the flyback has built-in diode (the newer "potted" type), try to reverse polarity of primary winding and see if the sparks are longer. If not, reverse it back.
Turn up the frequency until you just can't hear it (this is usually the best frequency to run your flyback at, but you can experiment). Now you can try slowly increasing the duty cycle (increasing output power), watch the transistor so it doesn't get very hot.
If you now can get a nice purple arc from the flyback, that can be drawn to few cm, your driver is working well. If not, something is probably fried (most likely the flyback itself).
Some pictures of my driver:
Circuit 2: Half-Bridge driver
Output power: Very high
Output voltage: Medium to low
The transistors need heatsinks, but these don't need to be large. Wind a primary of about 40 turns (of 0.5mm or thicker wire) around the exposed part of the core. Insulate the primary from the core well!
Something on resonance: All transformers have their resonant frequency, flybacks included. If your driver accidentally runs on the resonant frequency (or its harmonics) of your flyback, an excessive voltage builds up on the output from the flyback (which could theoretically rise many times the voltage the transformer can sustain), and the transformer literally bursts in flames.
For this purpose, I suggest to put a small lightbulb (40W) in series with the mains. Now, turn on the driver, and without drawing an arc from the flyback, adjust the frequency to where the lightbulb is darkest (the least current is drawn), this indicates you are safely away from resonant frequency (and its harmonics), because at resonance the current drawn is the highest. Make a few sparks with the flyback so you know it's working.
Now you can remove the bulb (or if you want to be safe, use a larger one until you remove it completely).
The power of this driver is mainly limited by your flyback, most flybacks start getting hot above some 300W. The arc generated using this driver is very hot and powerful, has appearance of a yellow/white flame, and can be drawn out in over 10cm in some cases.
If you want more power, you can try to remove some turns from the primary winding, but remember, removing turns raises resonant frequency, so frequency usually needs to be re-adjusted. Also watch the temperature of the transistors, they can get quite hot at high power after some while.
Video of arcs
Burning a CD