4-6 inch long cuttings are normally used. Any length or diameter can be rooted, from scrawny little woody twig to baseball bat and larger.  

Sterilize your pruners or knife to the best of your abilities. Make your cut above or below a NODE which is simply the joint where new branches, leaves and flowers grow from.
You can root the portions above the top two lines and they will produce cuttings that flower quickly. The portion between the green lines may or may not flower quickly. The portion below the bottom green line will have to develop new Y lateral growth to begin the FLORESCENT stage once again.

..............Now What?

Remove all but the smallest, new growth leaves so that your cutting can concentrate on root formation and not have to suffer the struggle to keep those heavy,  no longer needed, leaves alive.

The White spots will become future roots

The easiest way to root Brugmansia is to simply put the cuttings in a glass container, such as an ordinary drinking glass, and fill the container  3"-4" with ordinary room-temp tap water. Place the cuttings in the glass without overcrowding them. For those giant cuttings (length or diameter), you can use a bucket.

Never let the water get overly cold which happens in air-conditioned environments and when cutting are placed next to a window during the cold months. Never let the water get overly warm because your cuttings might cook and turn to mush. Fewer problems are encountered when cuttings are taken in June and July and water-rooted outside in a warm semi shady-shady environment.
Never let the water get old. The water should not be allowed to get cloudy, nor should it be a home for strange, wriggly critters. Refresh the water frequently.

Within a few short days you should see the bumps begin to pooch out (swell) and turn lighter in color. Some growers go ahead and pot the cuttings at this stage with great success. Others wait so long that the cuttings develop complex and interesting looking "root-beards", several inches long.  These roots can be severely trimmed with no visible trauma to the cutting or plant. 

Note: If your cutting begins to rot in water, salvage what you can by cutting the mushy part off (back to firm wood) and try a soil-rooting method. 

Another common method, that has been used for years by collectors who propagate large diameter cane cuttings of many different genera, is to lay the cutting length wise (horizontally) on top of sterile soil, leaving as many nodes/buds exposed to the sky as possible. Each node/bud is a possible new plant. If your cutting has the infamous little white bumps lightly press the whole length of the large diameter cutting into the soil, deep enough to prevent it from rolling around. For smoother woods and smaller diameters, completely cover the entire stem with soil leaving only the new growth exposed. Keep the soil damp but not soggy (much like leaving them to lay in the compost pile). Brugmansia cuttings with their pre-roots, nubbies, little white bumps and LENTICELS, are especially well designed and well suited for this method.

Note: You can lay those long lengths and large diameter canes horizontally in containers like those used to soak wall paper, filled with water. Or you can fill a 13 gallon or taller trash can with water and stand the cuttings on end, totally submerged. After you see the beginning signs of  pre-roots, nubbies, little white bumps  and LENTICELS, completely bury the cane horizontally, leaving only the buds and nodes exposed. Planted stem tip to stem tip - - -, a row of these rooted canes that  have several new growth stems on each one and that produce "similar in size and shape" flowers of various colors, would make a beautiful hedge. 
Two different canes planted side by side =  would make a beautiful stand-alone shrub/focal point, but you should choose brugs that have similar flowering periods.

Air layer & other rooting methods

How to root Brugmansia arborea species

Help!  How can I tell which end is the top and which is the bottom?