とりあえずマニュアルくらい嫁。

db=> create table test (time_field timestamp);
db=> insert into test values ('2001/08/31');
db=> insert into test values ('2002/05/31');
db=> insert into test values ('2002/08/05');
db=> select * from test;
time_field
------------------------
2001-08-31 00:00:00+09
2002-05-31 00:00:00+09
2002-08-05 00:00:00+09
(3 rows)

db=> select * from test where extract(month from time_field) = 8;
time_field
------------------------
2001-08-31 00:00:00+09
2002-08-05 00:00:00+09
(2 rows)

db=> select * from test where extract(day from time_field) = 31;
time_field
------------------------
2001-08-31 00:00:00+09
2002-05-31 00:00:00+09
(2 rows)