Without seeing your actual commands, it's difficult to know about the schema stuff...
Well, the "actual commands" is what the original question was asking for, since I really don't know how to do any of this (I find the documentation very unclear on the matter). At any rate, what I tried was
REVOKE ALL ON SCHEMA x FROM nopriv;
REVOKE ALL PRIVILEGES ON ALL TABLES IN SCHEMA x FROM nopriv;
...replacing x by public, pg_catalog, and information_schema.