Warm up your voice. Practice a few scales in lower chest voice to loosen up the vocal chords.
Sing the first five notes up a scale using a "me" sound in falsetto, starting at E above middle C. Sing the same notes back down the scale.
Repeat the 5-note scale, raising each starting note a half step once you've completed the previous pattern.
Practice singing "oo" sounds on a few patterns, then try "ah" sounds.
Keep your breath in your lower abdomen when singing. Keep your shoulders and body relaxed, and prevent your breath from starting in your chest cavity.
Practice singing the falsetto scale pattern with your voice forward in the top of your nose and sinuses. Then try singing the pattern with an open throat, similar to a yawn.
Practice transitioning from chest voice to falsetto and back, starting with octave notes. Repeat the transitions until they become more fluid and feel natural.