Take a deep breath.
Start singing, projecting from the upper throat instead of the chest. This will cause only the outer edges of your vocal cords to vibrate instead of your entire vocal cords, raising the pitch of your voice.
Hold a hand to your chest as you sing. If any part of your chest is vibrating, you are singing in your normal register.
Practice adding different styles and tonalities to adapt your falsetto voice to the kind of music you like to sing, whether it be rhythm and blues, progressive rock, heavy metal or alternative.