As best I can tell from that one picture, the plant is a Dracaena tarzana. It's often hard to tell from just one shot what exactly a plant is, but even if it's some other kind of dracaena, even some kind of yucca, the culture and pruning practices are the same.
The first thing to decide before you set out to prune a plant is 'how do I want it to look when I'm done?' The choices here would be tall, or short, and one cane, or more than one. (The long trunky, or stemmy thing is actually called a cane in these type of plants.) I think I'll describe the procedures for each of these choices in turn.
Before I begin, let me note that cane-type plants are great to do these kinds of procedures on, because they are so vigorous, and can sprout from dormant buds even when they appear to have been dried out and dead for years. One time I built a short, decorative fence by embedding a bunch of old corn plant canes in the ground. Don't you know, after about six months, my fence began to sprout! But I digress.
The elegant, horticultural thing to do would be to air layer. Arm yourself with a sharp knife, some damp sphagnum moss, some plastic wrap, rooting hormone, and electrical tape. Pick the point where you want the roots to start growing, say about seven feet from the top of the plant - that will give you a six foot tall plant after it's potted. Oh yes, don't forget to sterilize the knife with dilute bleach solution. Now, scrape away the top of the bark all the way around the cane, in a strip about 1" wide. Gently, now, only the very top part, the skin, so to speak.
Uh-oh, uh-oh, I hear some of you starting to cringe. Cutting? MY PLANT??? Okay, here's what you need to understand - cutting a plant, in terms of pain to the cuttee, is approximately the same as cutting your hair or fingernails...There.Is.None. It makes the plant more beautiful, if you do it right. If you don't, the plant just keeps on growing, and you get to try again another time.
Back to scraping the top layer of bark. After you've done that, rub a bunch - maybe 1/2 teaspoon - of the rooting hormone into the scraped area, and wrap it with moss. The moss should be damp, but not soaking - squeeze out all the water that will go. Wrap it into a nice fat clump all around the cane, then wrap plastic wrap around that, and secure the top and bottom tightly with the tape. There. You're done. Don't you feel accomplished?
Now, you and your plant just wait for a few months. Just keep an eye on the moss, if you see it's starting to look dried out, undo the tape and pour in a couple of spoons of water. But it should stay moist until the roots grow. If you want to see what all this looks like, try https://www.google.com/search?q=air+layering&hl=en&rlz=1C1CHUE_enUS486US486&tbm=isch&tbo=u&source=univ&sa=X&ei=g0lfUcG0HYK88ASCmYHoDw&ved=0CEEQsAQ&biw=1024&bih=475.
When the roots have nicely filled the bag of moss, cut the cane below the moss bag to free your now-shortened plant. This is probably the hardest part of the process, because some canes are thick and quite hard, and you may have to use a hand saw to do the cutting. Pot the plant with its new roots and shorter cane into your pre-selected beautiful container, or even better, into a plastic grow pot that you can place into your pre-selected beautiful container. This is called 'double potting,' and I have a video about that at http://www.youtube.com/watch?v=kG9PImILzh8
A word about soil. Please don't use those "moisture-retentive" mixes that some manufacturers are marketing. They do retain moisture, but that's a bad thing, because too much moisture in the soil is what kills most indoor plants. Use a cactus mix if you want, or a "soilless mix" if you can find it, or do some research and make a nice chunky, porous mix of your own. Try this http://forums2.gardenweb.com/forums/load/houseplt/msg0100030212371.html?11 to start research.
If your plant is already 10' tall, though, I think you probably have a good handle on its cultural requirements, and you already know about porous mixes and not overwatering, so I'll return to the pruning stuff. Now, if you want your plant to end up short, say 3 or 4 feet, do the air layering thing much closer to the foliage head; remember, you'll eventually be sticking about a foot of the cane-with-roots into the pot.
But what about the multi-cane thingy? This involves the not-difficult strategy of sticking one end of the cane, or piece of cane, into moist soil, and then being patient. As long as the soil is kept barely damp, the cane should sprout - not always, not every one, but a surprisingly high proportion of the time. In fact, you don't have to air layer at all, you can just cut the cane below the foliage, then bury the cut end in the soil. It's best to air layer a valuable plant, though, because roots might not form quickly enough to support all those beautiful leaves.
So okay, back at the big tall plant (or short, fat plant, if that's the way you shaped it) that you air layered into its new version, you've still got a long bare cane sticking out of the pot. Left to itself, it will probably sprout a bunch of new leaves, and keep right on growing. Or you could cut the long cane into 2 or 3 pieces - different lengths look best- put them back into the soil with the rooted piece, and see what happens. You can even cut the long cane into very short pieces, about 2" - each piece needs at least 1 scar where a leaf used to be - lay them horizontally under the soil, and wait for them to sprout.
So you can make yourself two new plants from the old one, or a whole bunch of new plants...next year's Christmas presents for all your friends! Please don't be afraid to prune.
Till next time,
Marlie - The Ficus Wrangler
(by Marlie Graves)