If your database is in the public schema, it is easy (this assumes you have already created the readonlyuser)

db=# \d
                                List of relations
 Schema |                        Name                        |   Type   | Owner
--------+----------------------------------------------------+----------+--------
 public   | users                                | table    | postgres
 public   | dogs                      | table    | postgres

You can use the following steps:

db=> GRANT SELECT ON ALL TABLES IN SCHEMA public to readonlyuser;
GRANT
db=> GRANT CONNECT ON DATABASE mydatabase to readonlyuser;
GRANT
db=> GRANT SELECT ON ALL SEQUENCES IN SCHEMA public to readonlyuser;
GRANT

If your database is using customschema,

db=# \d
                                List of relations
 Schema |                        Name                        |   Type   | Owner
--------+----------------------------------------------------+----------+--------
 customschema   | users                                | table    | postgres
 customschema   | dogs                      | table    | postgres

You should execute the above but add one more command:

db=> ALTER USER readonlyuser SET search_path=customschema, public;
ALTER ROLE