First of all you must get a Kuchipatchi. Unfortunately I'm not sure if there's any sure-fire way to get a Kuchipatchi. When training, try using only the third option- I believe this is for cheerfulness. Also I believe you must have a male Tamagotchi to get a Kuchipatchi. I'm not sure if that works because I have not tried it and I'm only making a wild theory, so please bear with me.
Secondly you must raise the bonding percentage to 100%, though use of bonding items, the Golf Putt and Shoe Pairs games or training.
Thirdly you must find someone else with a Yonepatchi, or continuously check the dating channel for one (you'll need a lot of patience to do this!). If you are using the dating channel and you don't get Yonepatchi and you've checked three times, you can check three more times if you set the time to 11.59pm and wait one minute, then set the time to the normal time and try again.
If that worked, your Kuchipatchi should evolve into Papapatchi and the Yonepatchi should evolve into Mamapatchi. They should have two eggs. I'm not sure exactly what they hatch into but I'm assuming the eggs will hatch into Futabatchi. After an hour, one baby should evolve straight into Kuchipatchi and the younger one should evolve straight into Chibipatchi.
Occasionally throughout the day you might see a random Family animation. Also when you press C, instead of seeing the animation influenced by bonding percentage, you might see the Kuchipa Family animation instead!