Take a deep breath and use this air to force the note you sing into your throat. This is the key to falsetto singing. To sing normally, you use your diaphragm. Falsetto singing is the opposite. Try singing the highest pitch you can reach and try to visualize pushing the note higher. This visualization process can help you push the note away from your chest and into your head.
Place your hand on your chest to ensure you're singing the note in falsetto. Your chest won't vibrate when you sing falsetto. You will feel a vibration in your head when you are singing the note in true falsetto. When you feel the note in your head, visualize again and open your mouth to take in more air. This air will push the high note you're singing even higher. If you feel strain on your throat, relax for a moment, then approach the same note with this method again. This is the way to increase your falsetto range, with the added benefit that it will add more volume to the note.
Sing the vowel sounds like a musical scale. Take a deep breath and start at the low end of your falsetto range, then work your way up on the vowels a-e-i-o-u-a-e-i. Just before you sing the i, take in another breath and sing the i. When the note comes out clearly, breath in and let the last note rise naturally. After some practice, you will be able to control this transition to a higher, more powerful falsetto range.