Stand up straight and breathe in using your diaphragm. The diaphragm is located just below your belly button, practice by placing your hand down there and feeling it expand when you inhale. You can do this by pretending that your stomach is a ball you are filling up, try to get as much air in it as you can. By doing this you get more air intake then you normally do with typical breathing. Every time you sing you should use this breathing technique.
Breathe in as much air as you can. Now push out the air inside your stomach and sing in your highest register, making sure to project the sound across the top of your throat as it leaves your mouth. Make sure you are not forcing it; it all has to do with where the sound bounces off of before coming out. If you do this correctly then your vocal chords will vibrate in the right place for singing falsetto i.e. the outer edges. Listen for rasp in your voice, if there is too much then reduce the pressure when pushing out.
Allow the air to go straight from your stomach to your head; this is how falsetto is achieved. If you are doing it correctly then you should feel vibrations on your head itself and not on your chest.
Challenge yourself now that you know the basics. Practice singing low falsetto, to your highest limit. Practice cleaning out the tone so that the sound you are producing is pure. Remember, anyone can sing in falsetto because it comes naturally, what takes time and patience is perfecting your falsetto and making it a pleasure to listen to.