So you want to improve your falsetto voice. If you are male, fine. If you're female, you don't have to except you are going to play a character role in a musical theater production.
Simply what is falsetto? Falsetto is a genuine, breathy tone on high notes. Come up with it as pure head voice, without some vibration or chest sound at all. An example most people have heard is a boy soprano. Women can achieve the sound without much complexity once they learn to use their upper vibrancy. So, ladies, you don't have to read any further if you don't need to.
Falsetto is so designated because it was once believed to be created by the false vocal collapses of the larynx. Modern laryngoscopy portrayed that it is in fact produced by the true vocal folds. When singing in falsetto the vocal folds are thinned, extended, and elongated so that they vibrate only at the margins. They do not fully close, which provides the breathy quality.
It is impossible to control dynamic changes (softness and loudness) on sustained notes when singing falsetto, because of the ineffective use of the vocal folds. Falsetto can be valuable when you're learning to use your head voice and upper resonance, but as soon as you have learned that you should use it most of the time instead of falsetto.
If after reading the above mentioned you're still concluded to develop falsetto, here is how to do it.
Begin with a good warm-up routine, and make certain you're using great posture and breath support. Try to counterfeit the sound of a boy soprano. Listen to some recordings to have the idea of the tone you're attempting to produce.
Go for a pitch in the upper part of your scale. On a hum, drop from your starting pitch up a fifth and back down: do so. Keep your tone light and hoot. Try similar pitches on "nee" and "nah". Then, move up a half-step and repeat the fifth slide up and down, again on the hum, "nee", and "nah". Keep on moving upward as far as you can without pressure.
All through the exercises, keep your face and mouth relaxed and free of tension.
If you desire to sing the high range with power and dynamics and you're not a natural tenor, you may bemore comfortable to have the song transposed to a lower key. If you can't develop the range without falsetto, maybe you just shouldn't be singing that range.
Falsetto can be used occasionally for artistic effect in a few songs, but it's not healthy to form a habit of it.