Database replication method

Hi all,
I'm new to PostgreSQL and generally to database engines
(background from MS Access but I started to learn PostgreSQL).

My question is about database architecture.
There is a small private school with 2 branches in 2 seperate locations.
Their database will manage student and teacher informations (contact informations, payments etc.)
Since a student or a teacher can go to both these two locations, database must be shared.
But, there might be failures to internet connections from time to time and I wonder how can we maintain data integrity after connection established.

Syncronization speed is not crucial. Mostly their data stays internal . I want (ideally):
2 Mirrored databases in 2 location, after an update they try to synchronise, if a connection occurs try later.

How can I do this with PostgreSQL?

Thanks,
Yuksel