Question about permissions on database.

Hello,
I wanna ask: is there a short way to giver permission to one user to
select/insert (all privileges) on whole database ?
Im create a user and try to give him all permission on existing
database, but when I try to select always got:
ERROR: permission denied for relation table_name

I simple do:
GRANT ALL PRIVILEGES ON DATABASE my_db TO my_user;
and when I do that my idea and what Im trying to do is to give all
privileges on for select, insert, update ... using sequences, exec
functions
to one user, but when I try to select, I receive error message:
ERROR: permission denied for relation table_name

I look at documentation and remained less scarred about how many grants
I should do for tables, for sequences, execution.
Im using postgresql 9.2

C.