This is a long one... look out!
Basic arm styling is for the most part a product of the body. When you're first learning arm styling, the emphasis should be on how to move the body correctly so that it causes the arms to react naturally.
Of course, not all arm movements are natural reactions to the body movement. When they're not, they will automatically draw attention to themselves. This can be good or bad -- If you were trying to draw attention to an arm gesture (eg waving a skirt, pointing, stroking your head with your hand), then you achieve the desired result. But if your arms are not working with the body simply because you don't know how to use them, then they draw the kind of attention to the arms you don't want, and you come across as awkward.
And while tricks and gestures can cover up quite a bit, unless you have a fully choreographed routine with every arm and hand movement mapped out, your awkwardness will ultimately show through. So it's best to learn your basic arm technique the right way first, before getting too involved in gestures. In other words, learn how to draw attention away from your arms before deliberately showcasing them.
Now basic arm styling that reacts naturally to the body is going to follow two main areas of movement: (1) Internal body actions, primarily from the muscles in the back, and (2) external actions of the body moving through space, such as spins, etc.
The first type of movement is where I'll focus my attention, because that accounts for most of the movement of the arms. This type of movement is constantly occurring throughout the dance, whereas the latter is something that is peppered sporadically, and is very case-specific. It can also be more intuitive, and in some cases doesn't even need to be taught. For example, if you're winding up for a spin to the right, you might tend to wrap the right arm across the body. That's an example of external actions motivating an arm movement.
So getting back to internal arm motivations: The arms are connected to your body at the top of the torso, with muscles connecting through the back. Therefore it is the activity through your back muscles which motivates the arms. If your back is not active and you are moving your arms all around, they will appear contrived and disjointed. So before you even bother working on your arms, you should be well versed in the use of your back.
If you go to the dance lesson on BallroomDancers.com entitled "Introduction Latin Hip Motion", you'll see an exercise for learning hip motion while standing in place (alternately bending one knee while straightening the other, etc). This exercise can also serve to improve back usage and then ultimately arm styling, depending on where you focus your attention.
For example, when you settle a hip to one side while keeping the shoulders level, you'll notice that one side of your body is stretched while the other is shortened. This is a natural result of the position of the hips, and doesn't necessarily require any deliberate, conscious usage of back muscles to achieve. However, when you do deliberately use the back muscles to assist the hips, you increase the activity in your back, and start the process of motivating the arms.
The muscle you should focus on the most is the latissimus, which is the broad muscle below the shoulder blade. When you settle a hip to one side without moving the shoulders, that side of the body "squeezes". Feel that muscle with the opposite hand, and see if you can give it an additioonal squeeze. Now as you shift the hips from one side to the other, instead of trying to move the hips to cause the back to squeeze and stretch, let the squeezing and stretching of the back be the force that motivates the hips.
Now for the arms: Begin with the arms streched out sideways. Now without bending the elbows or moving the arms anywhere (keep the hands fixed in space), try to rotate one arm in that position, in such a way as to cause the underarm to turn forward and upward, while at the same time rotating the other arm in the opposite direction so that the underarm turns down and backwards. Then rotate the arms in the opposite direction, so that they switch roles.
While you're doing this, try to isolate the activity as much as possible to the upper arm. You don't want to turn your writsts up and down, which is applying the activity to the forearms. You want the rotation to be occurring in the ball-and-socket joint where the upper arm meets the body. In fact, it's so easy to diminish the activity in the upper arm by fooling yourself with the forearm movement, that I suggest trying to keep the wrists perfectly still while doing this exercise. It's not that the wrists can't ultimately move with the arms, but that it's too easy to trick yourself into thinking you're doing more than you actually are. By keeping the wrists still, you force yourself to use only the upper arms.
Now let's connect the arms to the back and hips. Remember squeezing the latissimus muscles? That squeezing action should cause the upper arm to rotate under. On the opposite side, the back is stretching, and the arm is rotating back. Notice, then, that the back is the central point from which everything else is motivated. You squeeze one side, and the hip settles to that side, while the arm rotates under. Everything in the body is connected and working together, and this creates a natural type of arm movement.
Now in terms of the arm position, ultimately you won't need to keep them outstreched at your sides at all times. They can be in at your sides, or dropped down, or forward, or each arm in a different position... it doesn't really matter. Once you get a feeling for how the back motivates the arms, you can do it with the arms in almost any position. The key is in learning it in the first place, and during the learning process, (at least while doing the exercise, if not while dancing), I suggest using the outstretched arms. When the arms are in or elbows are bent, the forearms also get involved. This isn't a bad thing ultimately, but as I mentioned before, you can trick yourself into thinking you're doing more with your back-to-upper-arm connection than you really are. And once your forearms are waving all about *without* that connection, it starts to look contrived and phoney again. So use the exercise with the outstretched arms to keep yourself honest, and to keep a clear understanding of where natural arm movements really come from.
I hope this helps.
Regards,
Jonathan Atkinson
www.ballroomdancers.com