What GRANT USAGE ON SCHEMA exactly do?

GRANTs on different objects are separate. GRANTing on a database doesn't GRANT rights to the schema within. Similiarly, GRANTing on a schema doesn't grant rights on the tables within.

If you have rights to SELECT from a table, but not the right to see it in the schema that contains it then you can't access the table.

The rights tests are done in order:

Do you have `USAGE` on the schema? 
    No:  Reject access. 
    Yes: Do you also have the appropriate rights on the table? 
        No:  Reject access. 
        Yes: Check column privileges.

Your confusion may arise from the fact that the public schema has a default GRANT of all rights to the role public, which every user/group is a member of. So everyone already has usage on that schema.

The phrase:

(assuming that the objects' own privilege requirements are also met)

Is saying that you must have USAGE on a schema to use objects within it, but having USAGE on a schema is not by itself sufficient to use the objects within the schema, you must also have rights on the objects themselves.

It's like a directory tree. If you create a directory somedir with file somefile within it then set it so that only your own user can access the directory or the file (mode rwx------ on the dir, mode rw------- on the file) then nobody else can list the directory to see that the file exists.

If you were to grant world-read rights on the file (mode rw-r--r--) but not change the directory permissions it'd make no difference. Nobody could see the file in order to read it, because they don't have the rights to list the directory.

If you instead set rwx-r-xr-x on the directory, setting it so people can list and traverse the directory but not changing the file permissions, people could list the file but could not read it because they'd have no access to the file.

You need to set both permissions for people to actually be able to view the file.

Same thing in Pg. You need both schema USAGE rights and object rights to perform an action on an object, like SELECT from a table.

(The analogy falls down a bit in that PostgreSQL doesn't have row-level security yet, so the user can still "see" that the table exists in the schema by SELECTing from pg_class directly. They can't interact with it in any way, though, so it's just the "list" part that isn't quite the same.)

For a production system, you can use this configuration :

--ACCESS DB
REVOKE CONNECT ON DATABASE nova FROM PUBLIC;
GRANT  CONNECT ON DATABASE nova  TO user;

--ACCESS SCHEMA
REVOKE ALL     ON SCHEMA public FROM PUBLIC;
GRANT  USAGE   ON SCHEMA public  TO user;

--ACCESS TABLES
REVOKE ALL ON ALL TABLES IN SCHEMA public FROM PUBLIC ;
GRANT SELECT                         ON ALL TABLES IN SCHEMA public TO read_only ;
GRANT SELECT, INSERT, UPDATE, DELETE ON ALL TABLES IN SCHEMA public TO read_write ;
GRANT ALL                            ON ALL TABLES IN SCHEMA public TO admin ;

Well, this is my final solution for a simple db, for Linux:

# Read this before!
#
# * roles in postgres are users, and can be used also as group of users
# * $ROLE_LOCAL will be the user that access the db for maintenance and
#   administration. $ROLE_REMOTE will be the user that access the db from the webapp
# * you have to change '$ROLE_LOCAL', '$ROLE_REMOTE' and '$DB'
#   strings with your desired names
# * it's preferable that $ROLE_LOCAL == $DB

#-------------------------------------------------------------------------------

//----------- SKIP THIS PART UNTIL POSTGRES JDBC ADDS SCRAM - START ----------//

cd /etc/postgresql/$VERSION/main
sudo cp pg_hba.conf pg_hba.conf_bak
sudo -e pg_hba.conf

# change all `md5` with `scram-sha-256`
# save and exit

//------------ SKIP THIS PART UNTIL POSTGRES JDBC ADDS SCRAM - END -----------//

sudo -u postgres psql

# in psql:
create role $ROLE_LOCAL login createdb;
\password $ROLE_LOCAL
create role $ROLE_REMOTE login;
\password $ROLE_REMOTE

create database $DB owner $ROLE_LOCAL encoding "utf8";
\connect $DB $ROLE_LOCAL

# Create all tables and objects, and after that:

\connect $DB postgres

revoke connect on database $DB from public;
revoke all on schema public from public;
revoke all on all tables in schema public from public;

grant connect on database $DB to $ROLE_LOCAL;
grant all on schema public to $ROLE_LOCAL;
grant all on all tables in schema public to $ROLE_LOCAL;
grant all on all sequences in schema public to $ROLE_LOCAL;
grant all on all functions in schema public to $ROLE_LOCAL;

grant connect on database $DB to $ROLE_REMOTE;
grant usage on schema public to $ROLE_REMOTE;
grant select, insert, update, delete on all tables in schema public to $ROLE_REMOTE;
grant usage, select on all sequences in schema public to $ROLE_REMOTE;
grant execute on all functions in schema public to $ROLE_REMOTE;

alter default privileges for role $ROLE_LOCAL in schema public
    grant all on tables to $ROLE_LOCAL;

alter default privileges for role $ROLE_LOCAL in schema public
    grant all on sequences to $ROLE_LOCAL;

alter default privileges for role $ROLE_LOCAL in schema public
    grant all on functions to $ROLE_LOCAL;

alter default privileges for role $ROLE_REMOTE in schema public
    grant select, insert, update, delete on tables to $ROLE_REMOTE;

alter default privileges for role $ROLE_REMOTE in schema public
    grant usage, select on sequences to $ROLE_REMOTE;

alter default privileges for role $ROLE_REMOTE in schema public
    grant execute on functions to $ROLE_REMOTE;

# CTRL+D