Most brugmansias seem to be quite easy to take cuttings from, don't take the very softest of growth, look for stems with minute white dots on them, yes I know it sounds daft, but most of the older parts of the stems do have these white dots. Take a cutting about 4 to 6 inches long, remove some of the leaves, leaving about three, we find the best way is then to put the cuttings in a jam jar, with about 2 inches of water in the bottom. Change the water every couple of days or else it will become stagnant, after about 3 - 4 weeks you should see signs of roots starting to form from the white dots, when they are about an inch long you can carefully pot them up, the roots will be quite delicate, don't break them off. If the leaves begin too droop after potting up, you can reduce the amount of leaves, it will take the strain off the plant, until the roots establish themselves. The plant will soon grow away.
You can see the white dots (often called Nubbies) on the stem above the roots, this cutting is just about ready to pot up.
This is a picture of the same cutting, showing the leaves.