There is a technique for children's meditation here: http://www.learningmeditation.com/children.htm

Three seems pretty young for meditation. What if you focused on day-dreaming instead? Everyone else in her life is going to be pounding her to get her head out of the clouds and stay focused like a little drone, so why not be the one to encourage their imagination, so they won't be like everyone else and lose the ability to imagine and dream by the time they are 25 years old?

You're never too young (or too old) to dream.

I think that a three year old would do better to learn EFT. You can teach her the Single Handed or One Hand Tapping from Karen Nauman. as a way to destress right now. You can tell her about how important it is to only let happy thoughts in our head and that when we feel bad at all to tap on our fingernails. Practice dreaming up a wonderful future for you guys or her. Make the visualizing and tapping a game. Have her look at something and then close her eyes and try to see it in her head. When she gets negative, redirect her and give the words that are better. You can use some of the tapping points yourself on her, like gently tap the top of her head to help her calm down. Keep it simple, she is only three. As she grows and matures, your lessons can grow with her. And if you really want it to be meditation, maybe direct her. Let her clear her mind and see a blank white page for one minute. Then direct her to visualize something nice that she wants. Then talk her through a positive affirmation and maybe some tapping and then be done. She is three and doesn't need to meditate for very long. Also, make it a point to say your own positive affirmations outloud where she can hear you. Meditate where she can see you. Be an example and do and say what you want her to do and say, and she will pick it up. You may walk in on her meditating like you some time. Make it look fun. Make her want to do it.

Edit 7/18/11 Of course when teaching your sister, or anyone to replace negative thoughts with positive thoughts, that means that when she is angry, help her to replace anger with love. If she has reason to be angry, help her solve the problem, at her level. Teaching kids to pray is an excellent tool. If they are mad at their mom for not letting her have a cookie before dinner, teach her to pray and ask blessings for her mother. They must be kept short, sweet and simple, like, "Lord, please help my mom to be happy." That is good for a three year old. If someone is hurt, have her lay hands on them and pray, "Jesus, please touch my mom and make her neck not hurt, amen." Don't push her if she is not intereste, just say, "Ok, I will then," and then do it in front of her. Eventually she will be interested. If she gets hurt, pray for her. When she is upset, help her find and visualize a happy place.

There are a group of Musicians (U2,Sheryi Crowe and many others) who in the near future will perform a series of concerts, and with the proceeds from these concerts they have a vision to teach One Hundred thousand children globally, to meditate inside one year. And all those children will agree to each teach ten other children to meditate and so on. At that rate this planet should calm down in a very short span of time. There's a great dream. Love and Light

it depend what kind of meditation you want to teach them. also know this some can learn it by them self. and those that learn it by them self are over all that can be teached.