Well there are different kinds of families. I'm going to say how to get them and their family pets. Here goes:
Mame family- Marry your Mametchi with someone else's Chantotchi (doesn't matter if it's from the dating channel). You must have 100% bonding by the time the Mametchi marries. If this works, you should have two children that evolve straight into Mametchi and Chamametchi after the baby stage. The family pet, Bagubagutchi, shows up at certain times when you press C.
Meme family- Marry your Memetchi with someone else's Mumutchi (doesn't matter if it's from the dating channel). You must have 100% bonding by the time the Memetchi marries. If this works, you should have two children that evolve straight into Memetchi and Imotchi after the baby stage. The family pet, Chitchi, shows up at certain times when you press C.
Kuchipa family- Marry your Kuchipatchi with someone else's Yonepatchi (doesn't matter if it's from the dating channel). You must have 100% bonding by the time the Kuchipatchi marries. If this works, you should have two children that evolve straight into Kuchipatchi and Chibipatchi after the baby stage. The family pet, On Sen Moguratchi, shows up at certain times when you press C.
Furawa/Violet family- Marry your Furawatchi/Violetchi with someone else's Sukatchi (doesn't matter if it's from the dating channel). You must have 100% bonding by the time the Furawatchi/Violetchi marries. If this works, you should have two children that evolve straight into Furawatchi/Violetchi and Kizatchi after the baby stage. The family pet, Hanatarezoutchi, shows up at certain times when you press C.
Smart family- Get a Tamagotchi adult that evolves into either Mamametchi or Papamametchi. Marry it with another Tamagotchi adult that evolves into the other gender Mame-family parent (e.g. if you have a Tamagotchi that evolves into Mamametchi, marry it with another Tamagotchi that evolves into Papamametchi). If this works, the babies should all be Mimifuwatchi (I don't think it matters how many babies you get).
Cheerful family- Get a Tamagotchi adult that evolves into either Mememamatchi or Memepapatchi. Marry it with another Tamagotchi adult that evolves into the other gender Meme-family parent (e.g. if you have a Tamagotchi that evolves into Mememamatchi, marry it with another Tamagotchi that evolves into Memepapatchi). If this works, the babies should all be Pantsutchi/Omututchi (I don't think it matters how many babies you get).
Easygoing family- Get a Tamagotchi adult that evolves into either Mamapatchi or Papapatchi. Marry it with another Tamagotchi adult that evolves into the other gender Kuchi-family parent (e.g. if you have a Tamagotchi that evolves into Mamapatchi, marry it with another Tamagotchi that evolves into Papapatchi). If this works, the babies should all be Futabatchi (I don't think it matters how many babies you get).
Ninja/Shinobi family- Get any set of Tamagotchi adults and let their happiness hearts drop a lot. Try not to let their hunger hearts drop too much though.
Petit/Puchipuchi family- Get any set of Tamagotchi adults and let their hunger hearts drop a lot. Try not to let their happiness hearts drop too much though.
Large/Dainamikku family- Get any set of Tamagotchi adults and feed them meals when their hunger hearts are full, until they won't eat any more. Keep doing this to get the large/dainamikku family.
Blended family- Marry your Tamagotchi any way you want and hopefully you will get the blended family.
Space family (not sure if that's its proper name)- Marry your Tamagotchi with another Tamagotchi from a different region. What I mean is, for example you could mate an American v5 with the Japanese Famitama, or an European v5 with an Australian v5, or an Australian v5 with an American v5... I'm not usre if Asia and Australia are counted as the same region on the v5 because on TamaEXPO Australia and Asia share the same pavilion and in surveys there is a box for Australia and Asia. Another way to get the space family is to get your bonding percentage to 100% and keep checking the dating channel. Hopefully Puranetchi/Planetchi will show up in place of the Matchmaker and offer Sanitchi/Sunnytchi. Accept the marriage and the baby should be an Iwatchi.