You can become better at this by doing it a lot. Every time a situation presents itself where you can try to convince someone of something, try to do it just for the heck of it. Most people evade these situations, but if you keep at it, it will improve.

Persuasion is independent of "shyness" (actually, being an introvert) but a lot of it has to do with natural talent, unfortunately [1]. You can definitely improve it, but some people are just born with a higher degree of "energy transitivity". For instance, their face have more muscles and they're wired in such a way that it is easier for them to control it, among other things.

[1] Malcom Gladwell wrote about this briefly in "The Tipping Point". You can learn more on this by looking up the book "Emotional Contagion" by Elaine Hatfield, John Cacioppo and Richard Rapson. There's also Howard Friedman, from the University of California, who created the Affective Communication Test, which aims to give an individual a measure of his personal carisma - this transmissive or "magical" ability you speak of: http://www.faculty.ucr.edu/~friedman/act.html