Tamagotchis should be cared for like any other pet; with lots of attention and love.
The icons around the Tamagotchi screen show what the pet needs to stay alive and happy. These icons vary between different types of Tamagotchis, but there's always a way to feed and play with the pet, as well as clean up its messes. There's also an icon for alerting the caregiver that the pet needs something.
Every Tamagotchi goes through a daily cycle of eating, pooping, playing, and sleeping. These are the basic things that a Tamagotchi does. The caregiver's job is to keep up with these needs so that the pet is happy and healthy for a long time.
Some Tamagotchis have events that occur during its life cycle. Some of these events include daily routines like brushing teeth and bathing, or random occurances like attacks from other creatures.
Tamagotchis typically follow a linear growth pattern based on the type of care they have received. Good care produces happy characters, and poor care produces sickly characters who don't live very long.
A newer aspect of Tamagotchis is the ability to connect with other pets and devices. They connect to play and mate with other Tamagotchis, and to download extra goodies like snacks and games.