I have the query In Oracle SQL:
       select town_name, 
              regexp_substr(town_name, '[^A,]+', 1, 1) as c1,
              regexp_substr(town_name, '[^A,]+', 1, 2) as c2, 
              regexp_substr(town_name, '[^A,]+', 1, rownum) as c_rownum,
              rownum
          from epr_towns
The first 2 rows from the result are:
VALGANNA        V   LG  V   1
VARANO BORGHI   V   R   R   2
I need to obtain the same result on PostgreSQL (for the row with regexp_substr(town_name, '[^A,]+', 1, rownum) as c_rownum), and I don't know how. 
Could you help me?
Thanks.
There's really two separate problems here
To solve for rownum, use a CTE (WITH clause) to add a rownum-like column to your underlying table.
regexp_matches works a little differently than Oracle regexp_substr.  While Oracle regexp_substr takes the nth match as an argument, PostgreSQL regexp_matches will return all matches as a table-valued function.  So you have to wrap the call in a subquery with limit/offset to pluck out the nth match.  Also, the rows returned by regexp_substr are arrays, so assuming you have no parenthesized expressions in your regexp, you need to index/dereference the first item in the array.
End result looks like this:
http://sqlfiddle.com/#!17/865ee/7
 with epr_towns_rn as (
    select town_name,
      row_number() over(order by town_name) as rn
  from epr_towns
)
select town_name,
   (select (regexp_matches(town_name, '[^A,]+', 'g'))[1] offset 0 limit 1) as c1,
   (select (regexp_matches(town_name, '[^A,]+', 'g'))[1] offset 1 limit 1) as c2,
   (select (regexp_matches(town_name, '[^A,]+', 'g'))[1] offset rn-1 limit 1)
     as c_rownum,
   rn
   from epr_towns_rn;
If you only wanted the first match, you could leave out the 'g' argument and leave out the limit/offset from the subquery but you still need the subquery wrapper in case there's no match, to mimic regexp_substr returning null when no match.
I don't have a table, so I use generate for example:
   select town_name, 
          regexp_substr(town_name, '[^A,]+', 1, 1) as c1,
          regexp_substr(town_name, '[^A,]+', 1, 2) as c2, 
          regexp_substr(town_name, '[^A,]+', 1, dense_rank() over (order by town_name)) as c_rownum,
          dense_rank() over (order by c)
      from epr_towns
I believe you look for dense_rank window function?..
NB. it is always easier to have SQL fiddle or initial code
You can find your case and other scenarios on this page: https://pgxn.org/dist/orafce/doc/sql_migration/sql_migration03.html
--
In short you can do something like that: from OracleDB:
SELECT
    REGEXP_SUBSTR('one two three four five ',
    '(\S*)\s') AS "REGEXP"
FROM DUAL;
Result: one
to PostgreSQL:
SELECT (
    SELECT array_to_string(a, '') AS "REGEXP"
    FROM regexp_matches('one two three four five ',
    '(\S*)\s',
    'g') AS f(a)
    LIMIT 1
);
Result: one
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