Copy PostgreSQL data from one PC to another
You could dump the database using pg_dump and then restore it on the new server using psql. Here's a couple of commands from the above link:

Create the backup:

pg_dump mydb &gt; db.sql

Copy db.sql to the new server (specific command depends on OS)

Go to the new server

createdb mydb -E UTF8 (you don't have to specify UTF8 encoding, but I always do)

Then:

psql -d mydb -f db.sql

As I was answering, JohnP just answered with a fine answer but assumes that pg_hba.conf has been edited to allow remote connections and postgres.conf has been edited to listen on the network.