Getting poinsettia to bloom again is not complicated but it does demand specific cultural controls with little room for error. We'll assume you've grown your poinsettia since last Christmas and you've fed it properly with lots of light - it has grown into a small shrub and you want to get it to bloom again.
Short Day Plants - Poinsettia are referred to as "short day plants" and they require a night time (lack of sunlight) of 11 hours and 45 minutes to initiate flowering. So as our summer days shorten towards fall, the increasing length of night triggers flower formation. This assumes a temperature of 65F. If the temperatures are lower (say 62F) then the time of sunlight deprivation will be longer - in this example 13 hours of night.
Cooler temperatures will require longer nights. And temperatures above 70F will create a similar situation - too high a temperature requires longer night hours.
12 Hours - Generally, in the home environment you need night darkness of 12 hours for good and fast flower formation. And you require this night darkness for approximately 6 weeks starting in mid-September. After this, you only require regular day length (whatever that is in your location)
No Light At All - If you put lights onto the poinsettia leaves (even for a few seconds during this 6 week period) at night -photosynthesis will start and the plant will "wake up" and the dark requirements will not be met. In this case it will not flower! Research shows that light as low as 1-2 foot candles will trigger growth. There is some data indicating a few seconds of light will put the plant back an hour or more.
(As a side note -this is why some greenhouses in urban areas can no longer grow poinsettia. Traffic moving past the greenhouses at night throw headlight beams onto the plants and wake them up and street lights can be a major problem if they don't use artificial shading on the plants.)
Full Sunshine - Getting a poinsettia to bloom again requires full, bright sunshine. Anything less will reduce flowering. In the home, this translates to a full south window (squeaky clean) or supplemental grow-lighting. Low light levels will also produce small bracts.
Soil - Soil should be a high quality artificial mix. No garden soil as the soil has to be well-drained. Usually I recommend a good garden mix with plenty of compost but in this case I have had much more luck with an artificial mix.
Temperature - House temperatures should be in the 65-70F range during the night and 80F during the day for best flowering.
Mat It - You might want to sit the pot on a propagation mat for the day to heat up the roots if you can't heat up the entire room. Lower temperatures during the daytime will either impede flowering or eliminate it.
Feeding - Commercial growers feed with every watering in dilute concentrations but home gardeners can get their poinsettia to bloom again by feeding a balanced houseplant food once a week at full strength. Failure to feed will produce tiny bracts.
Pruning - Getting a poinsettia to bloom again means proper pruning in the home. The second week of September, cut all weak and spindly growth from the plant and pinch the remaining growing stems to leave 4 to 6 leaves or leaf nodes per stem or branch. On short plants, you can simply leave 4 -6 leaves to survive and top cut the rest of the plant off.
Humidity - Maintain a high humidity for the plant if possible. Keep feeding. The plant should throw shoots and by the third week of September, those shoots should be one-inch long.
Keep feeding and watch for insects. It is at this point that whiteflies attack poinsettia and you can control them with soap only until the color starts to show on the bracts. If you spray soap on colored poinsettia leaves, they do not respond well (burning). Other common pests include mealybugs and thrips.
If you maintain the temperature, full light environment, watering and feeding, you should see color by the middle of November. Any deviation from the guidelines above and flowering will be delayed.
The schedule looks like this
January through mid-September - grow Poinsettia in full sunlight, feed at least once a week and water when needed.
Mid-September - prune back as above
Mid-September - begin temperature regime as above
Mid-September - 12 hours of darkness and 12 hours of full sunshine as above for at least 6 weeks
End of October - can go into full sunshine all day long with normal night time darkness.
Mid-November - you should start to see color in bracts
Maintain warm temperatures
Rinse and repeat for as many years as you can....