How can I get my Easter (Sunrise), Christmas, Thanksgiving cactus to

The plants known as Holiday Cactus, Lobster Cactus, Xmas Cactus, Sunrise Cactus, and many other names, belong to several genera of jungle cacti but can generally be treated alike. All are true cactus plants, some have small spines in the aeroles, and the flowers grow on last year's growth. These plants are generally segmented and flat, and roots form between the segments for easy propagation.
These plants come from the jungles of Central and South America and therefore cannot store water like their cousins from the deserts can. Instead, they rely on almost daily rains, and enter a semi-dormancy period when the short dry season comes. For most of the species concerned, this dry season occurs in the short-day period so that the combination of short days and cooler nights leaves these plants drier but not dessicated.
The soils of these usually epiphytic plants consists of decayed leaves, insects, pieces of bark, etc., generally anything the wind or birds leave in the crotches of the trees or on the ground below. In cultivation, the stone/gravel/sand mix for desert cacti is supplanted by peat/leafmold/loam for these. The difference is high organic matter, the similatity is that both kinds of cacti need well -draining mixes.
Once the right soil has been given, it is important to note that full sun in the summer is not a good idea in most places, but that some sun is needed. When the days grow short (Sep/Oct in northern hemisphere), water sparingly, giving the plant about 6 weeks of a cooler, drier regimen. This period will induce bloom, especially if the diurnal range is in the 20-30 degree F range, something hard to do in the average home.
Although some thought can be given to shading the plants from bright lights at night, this does not seem as critical as the rest period. More important is to shelter the plant from dry winds (heating ducts), changing the environment once buds have set, and ethylene gas (from plastics, propane heaters and ripening fruit). Any of these three conditions can cause the falling off of the flower buds, commonly called bud blast.
The small roots of these cacti are not equipped to deal with drought, and the stems have adapted to living in the shade cast by their tree hosts. Given even a rough approximation of their jungle home they will bloom in a panoply of colors, in season, every year.