I assume you are talking about one of the many Euphorbia... The area need's to air dry. & apply 0.1% IBA (Rooting hormone) stick in well drained (damp)soil
The smaller the "cut/broken" area (cross section) the easer it is to root.

I have a huge african milk tree but need to trim it down. I'm paranoid about clipping it and wonder what area of the plant the clipping should be done. Any suggestions?

I have one of these that is at least 25 years old. It is so easy to root. Just break off one of smaller side branches that is 4 to 6 inches long, let the end dry a bit and stick it in a pot that has a coarse soil in it (Cactus mix works very well). Its Latin name is Euphorbia trigona. The trick with these is to water only when the pot is dry. They hate wet feet!
I have seen these cut back and to my mind, they look awful afterwards. I think you might be better off starting a new plant.