*Topic moved to 'Help for Tamagotchi Owners'*
Alright, now this one I know how to answer exactly!
There is no traditional Pause function like in older versions. Instead once your Tama is at the child stage or older, you can take them to the TamaHotel. To do this, travel to the hotel under the "Travel to Other Town" menu (looks like a ship) and once there, scroll down until you find the "Leave" option. Press on that.
Some dialogue will happen then you'll be asked if you want to leave your Tama or not. Choose the "yes" option.
Now your tama will be there until you pick them up, or until two hours before their bedtime, or until you run out of money. Whatever happens first.
You'll be charged 10 Points per hour, and winning one game will give you 200 points, so that's 20 hours right there.
After your Tama is on Generation 2 or further, you can do the Hotel still or you can drop the Tama off at its parents' house for the same services but for Free!
EDIT: Forgot to mention, doing the hotel or parents daycare things will
not delay growth or ageing! So you don't need to worry about throwing grow and age times all out of wack!