From your other thread I know that you realize you can buy bonsai that are already underway so I'll skip over that for now.
I'd gathered that taking a cutting meant weighing down a branch of the tree to the ground for a few months so that roots will form and then cutting that part off.... is that what you're talking about?
That technique is known as layering and is a traditional way or propagating new material. A cutting is simply a shoot or young branch that is cut from the donor plant and encouraged to grow new roots. Neither of these techniques are exclusive to bonsai.
Not sure if I got my vocab. mixed around, or if there's a simpler way to start a bonsai from a live tree around me.
You can acquire subjects for bonsai from numerous sources, you need not start from seeds or cuttings. It is a common misconception that the fine old bonsai seen displayed were grown from very young material. Sometimes this is so but more often older, larger material is selectively pruned. Rather than grow a bonsai up cut one down.
A nursery is a good place to start. You can almost always find something to work with. You will probably not be able to differentiate exceptional material from the average but at your early stage of interest just getting your feet wet is more important than finding exceptional material.
Overgrown landscape plants is another source of stock that can yield good material. Often such material can be obtained for little or no cost. I have found material that has been discarded at the local yard wast repository. Friends, knowing of my interest, have brought me material. Keep your eyes open and you may get lucky.