These are the methods I find work for me when taking Brugmansia cuttings.
Rooting in Water
This method works well with hardwood cuttings, and some greenwood cuttings.
Take off all but the two top leaves.
Place into a glass jar with approx 2 inches of water.
Change the water everyday.
Do not put into direct sunlight.
No leaves should be submerged in the water. The leaves will rot.
When white nubbles (lenticels) appear on the cutting you can remove from the water and plant up.
Place in a good soil mix with plenty of perlite.
It is very important that the plant has good drainage.
Do not over water at this stage, or your plant will rot.
The plant may wilt, after the shock of being taken from the water.
It will soon perk up again when it adjusts to the soil.
Do not feed until there is a good root system.
Then half strength for the first few weeks.
Wood Cuttings
Also called log cuttings.
Take a cutting approx 2 to 8 inches long.
Fill your pot with a good quality soil with plenty of perlite.
The size of pot will be governed by the size of cutting.
Make a line in the soil with your finger or dibber around half an inch deep.
Place the cutting length ways into the the soil. Half the cutting should be below the soil, the other half above the soil.
Water very lightly.
The longer the cutting might produce several new plants.
When they sprout, let them grow a few inches high then make a clean cut either side of your new plant.
Plant into good soil and perlite mix.
Do not over water.
Rooting in Soil
This method works well with hardwood and soft wood cuttings.
Fill a clean pot with a good quality soil with plenty of perlite for drainage. Most important.
Make a hole in the soil and place the cutting into it.
Water the cutting so that the space around it is filled in with soil.
Do not put into direct sun light.
Your cutting will root quicker if placed on something warm, such as a heating mat.
Do not water until the soil feels dry to touch.
Very wet soil will rot your plant.
Note on Cuttings
I have stated that cuttings can be taken in Spring or Autumn, they can actually be taken any time when the plant is not dormant. After care can be more difficult with Autumn cuttings as they do not have much time to get established before Winter.