Ollyc's answer is good as it is not Postgres-specific, however, it breaks down when the foreign key references more than one column. The following query works for arbitrary number of columns but it relies heavily on Postgres extensions:
select
att2.attname as "child_column",
cl.relname as "parent_table",
att.attname as "parent_column",
conname
from
(select
unnest(con1.conkey) as "parent",
unnest(con1.confkey) as "child",
con1.confrelid,
con1.conrelid,
con1.conname
from
pg_class cl
join pg_namespace ns on cl.relnamespace = ns.oid
join pg_constraint con1 on con1.conrelid = cl.oid
where
cl.relname = 'child_table'
and ns.nspname = 'child_schema'
and con1.contype = 'f'
) con
join pg_attribute att on
att.attrelid = con.confrelid and att.attnum = con.child
join pg_class cl on
cl.oid = con.confrelid
join pg_attribute att2 on
att2.attrelid = con.conrelid and att2.attnum = con.parent