You're misreading the docs slightly. some_firm.client.new is creating a new Client object from the clients collection, and so it can automatically set the firm_id to some_firm.id, whereas the docs are calling Client.new which has no knowledge of any Firm's id at all, so it needs the firm_id passed to it.
The only difference between some_firm.clients.new and some_firm.clients.build seems to be that build also adds the newly-created client to the clients collection:
henrym:~/testapp$ rails c
Loading development environment (Rails 3.0.4)
r:001 > (some_firm = Firm.new).save # Create and save a new Firm
#=> true
r:002 > some_firm.clients # No clients yet
#=> []
r:003 > some_firm.clients.new # Create a new client
#=> #<Client id: nil, firm_id: 1, created_at: nil, updated_at: nil>
r:004 > some_firm.clients # Still no clients
#=> []
r:005 > some_firm.clients.build # Create a new client with build
#=> #<Client id: nil, firm_id: 1, created_at: nil, updated_at: nil>
r:006 > some_firm.clients # New client is added to clients
#=> [#<Client id: nil, firm_id: 1, created_at: nil, updated_at: nil>]
r:007 > some_firm.save
#=> true
r:008 > some_firm.clients # Saving firm also saves the attached client
#=> [#<Client id: 1, firm_id: 1, created_at: "2011-02-11 00:18:47",
updated_at: "2011-02-11 00:18:47">]
If you're creating an object through an association, build should be preferred over new as build keeps your in-memory object, some_firm (in this case) in a consistent state even before any objects have been saved to the database.