You have to wait until generation 2 on your Tamagotchi, and take absolute perfect care. It's really simple.
If you take perfect care on the first generation, you'll keep getting Mametchi. By the second generation, you should get a Mimitchi.
EDIT:// This is usually only on the Version 1 or 2. I'm not completely sure how to get it on the higher versions, considering there are so many characters. You may ask someone else that knows more about Tamagotchi's.