As a supplement to the other answers, even a SELECT statement that returns no rows will expose the column names to you and to application code.

select *
from table_name
where false;

Permissions might come into play with any of these approaches.

The information schema is the slow and sure way: it is standardized and largely portable to other databases that support it. And it will keep working across major versions.

However, views in the information schema often join in many tables from the system catalogs to meet a strictly standardized format - many of which are just dead freight most of the time. This makes them slow.
The Postgres developers aren't making promises, but basics (like what is needed here) aren't going to change across major versions.

psql (the native command-line interface) takes the fast lane, of course, and queries the source directly. If you start psql with the parameter -E, the SQL behind backslash commands like \d is displayed. Or \set ECHO_HIDDEN on from the psql command line. Starting from there you can build an answer to your question.

Given one table, is it possible to have a list of the names of the columns for this table.

SELECT attrelid::regclass AS tbl
     , attname            AS col
     , atttypid::regtype  AS datatype
       -- more attributes?
FROM   pg_attribute
WHERE  attrelid = 'myschema.mytable'::regclass  -- table name, optionally schema-qualified
AND    attnum > 0
AND    NOT attisdropped
ORDER  BY attnum;

Faster than querying information_schema.columns. Try EXPLAIN ANALYZE to see for yourself. Still hardly matters for a one-time look-up. But might make a difference if used in a query / function that's repeated many times.

There are also subtle differences in visibility. Detailed comparison:

• How to check if a table exists in a given schema

psql on PostgreSQL 11+

If you're looking for the column types on a query, you can use psql's \gdesc

SELECT
    NULL AS zero,
    1 AS one,
    2.0 AS two,
    'three' AS three,
    $1 AS four,
    sin($2) as five,
    'foo'::varchar(4) as six,
    CURRENT_DATE AS now
\gdesc
 Column |         Type         
--------+----------------------
 zero   | text
 one    | integer
 two    | numeric
 three  | text
 four   | text
 five   | double precision
 six    | character varying(4)
 now    | date
(8 rows)

PostgreSQL only

This is somewhat hokey but could be a contender if you are looking for the shortest possible SQL:

SELECT json_object_keys(to_json(json_populate_record(NULL::schema_name.table_name, '{}'::JSON)))

or even shorter (assuming there is at least one row present in the table)

SELECT json_object_keys(to_json((SELECT t FROM schema_name.table_name t LIMIT 1)))

The listing preserves the order. In case you don't care about the order and have hstore extension installed you can do even shorter

SELECT skeys(hstore(NULL::schema_name.table_name))