I wouldn't do it this way but you want it simple so do this. To make ready, take a piece of paper towel and fold it on itself so that you have a strip about 2 inches wide and 10 inches long. You probably have a roll of plastic wrap around the house. Have a twisti at hand. Finally a piece of black craft paper. Now here we go- wet the paper towel strip in a glass of spring water; take a cutting from the plant; wrap or rather roll the paper towel strip around the cutting, making sure the cut end is covered. Wrap the plastic wrap around the towel to and loosely secure with a twisty to preserve moisture; then place the black craft paper on a window sill that gets moderate but not direct sunlight. Lay the bagged cutting down with the bagged part lying on the black paper. The black paper will make the bagged section warmer than the rest of the cutting and enhance root growth. Check weekly by opening the bag to check for root growth and to keep the towel most. When you do see the START of rooting place the cutting in a pot of potting soil by poking a hole in the soil and gently cover being careful not to harm the roots and keep it in moderate light. There you go. I kept it simple with things you can find around the house. You didn't have to go to the garden center to buy rooting hormone or vermiculite, sphagnum moss, or plastic plant starter tents. Let's hope simple makes successful. But don't start right away! Wait a while for other members to give you some other ideas before you start. By the way, this is the classic office plant. I had one that touched the ceiling in my office just on fluorescent lighting alone. Best Regards and Good Luck!

Or alternatively, if your plant is Schefflera arboricola (google to see pics) then cut off the tops, about 8 inches long, strip off the lower leaves, leaving two pairs towards the top, pop the stem/s in a bottle of water sitting on a windowsill (out of sun) so that the leaves and the top parts are not immersed, keep the water topped up, and wait about 6 weeks, by which time the bottle should have quite a mass of roots visible - which is when you pot it up.

Bamboo, will S. taiwaniana propagate the same way? Mine is about 15 inches of bare stem, with about 8 sets of this year's leaves at the top. All of last year's leaves have fallen.
It's planted in a clay soil outdoors and has been there since May 2013.

Loosestrife: I am waiting on different comments. Thank you for your input. It does sound simple. When "taking a cutting from the plant"... do I just break a limb off? I did read that you were suppose to cut the top off... I am very Unknowledgeable when it comes to this kind of thing. So...how do I cut the top... will it damage it... will it stop growing up and start bushing out? I do not want to cause damage to the plant. It is so pretty now.
Like I say-- I'm not a gardener!
I do love this website!
Thank everyone for your help and patience.

@Teadrinker - yes on Schefflera taiwaniana and other cold hardy Scheffies. I know a few folk who have rooted them in water.

Take a scissors or a box cutter (you know the plastic handled ones they sell everywhere ) an cut a stem off that has a cluster of leaves on it and stick it in a glass of water, place it in a lighted window and wait. In a few weeks you will see roots , then stick it into a pot of soil and in another few weeks you will see tiny leaflets sprouting from the stem. There are two types of sheffleria plant one large and one(dwarf) either way the procedure is the same in your case ( not a gardener).

Secateurs, and is it my imagination, me going bonkers, or am I seeing in stereo! I seem to have repeated my answer 'without moving my lips' so to speak, or in this case, rephrasing it somewhat and not actually typing it in. Loosestrife - are you not now saying what I said originally, as opposed to what you suggested in the first place?

Yup. In my haste this morning I omitted saying do what bambo said to do. Unintentional plagiarism. When she mentioned tearing off a stem I thought best to give a suggestion of simple household cutting tools to use. Then I thought maybe my paper towel method would be too complicated since she sounded kind of jitterish so I mentioned the glass of water without giving you the full credit deservedly due to you. Grandmother, since you are admittedly not a gardener I assumed that you do not have secateurs (also known as pruning shears) in your kitchen everything drawer nor are you about to buy them for a once in your life use so I suggested a scissors or the common box cutter which is in almost everyones kitchen everything drawer.

Erm, 'cutting' off a stem, not tearing... I've always wondered what Americans call secateurs, for I've never heard them use the term. If pruning shears are secateurs, what are pruning shears called (also known as hedging shears, clipping shears or just shears) Loosestrife?

For the short stuff (taking cuttings) pruning shears or pruning clippers. For the big stuff, hedge shears Or hedge clippers. In the USA" secateurs"is never used and that's the way it is.

Secateurs is from the French secateur, meaning to cut, so I rather wonder what the French speaking Canadians call them...