List tables in a PostgreSQL schema

In all schemas:

=> \dt *.*

In a particular schema:

=> \dt public.*

It is possible to use regular expressions with some restrictions

\dt (public|s).(s|t)
       List of relations
 Schema | Name | Type  | Owner 
--------+------+-------+-------
 public | s    | table | cpn
 public | t    | table | cpn
 s      | t    | table | cpn

Advanced users can use regular-expression notations such as character classes, for example [0-9] to match any digit. All regular expression special characters work as specified in Section 9.7.3, except for . which is taken as a separator as mentioned above, * which is translated to the regular-expression notation .*, ? which is translated to ., and $ which is matched literally. You can emulate these pattern characters at need by writing ? for ., (R+|) for R*, or (R|) for R?. $ is not needed as a regular-expression character since the pattern must match the whole name, unlike the usual interpretation of regular expressions (in other words, $ is automatically appended to your pattern). Write * at the beginning and/or end if you don't wish the pattern to be anchored. Note that within double quotes, all regular expression special characters lose their special meanings and are matched literally. Also, the regular expression special characters are matched literally in operator name patterns (i.e., the argument of \do).

You can select the tables from information_schema

SELECT * FROM information_schema.tables 
WHERE table_schema = 'public'

Alternatively to information_schema it is possible to use pg_tables:

select * from pg_tables where schemaname='public';

For those coming across this in the future:

If you would like to see a list of relations for several schemas:

$psql mydatabase
mydatabase=# SET search_path TO public, usa;   #schema examples
SET
mydatabase=# \dt
              List of relations
 Schema |      Name       | Type  |  Owner
--------+-----------------+-------+----------
 public | counties        | table | postgres
 public | spatial_ref_sys | table | postgres
 public | states          | table | postgres
 public | us_cities       | table | postgres
 usa    | census2010      | table | postgres

If you are interested in listing all tables in a particular schema, I found this answer relevant :

SELECT table_schema||'.'||table_name AS full_rel_name
  FROM information_schema.tables
 WHERE table_schema = 'yourschemaname';