How do I alter my existing table to create a range partition in Oracle

If you are using Oracle 12c Release 2 you could use single ALTER to convert non-partitioned table to partitioned one (this is one way trip):

CREATE TABLE my_tab ( a NUMBER(38,0), b NUMBER(38,0)); 

ALTER TABLE MY_TAB MODIFY PARTITION BY RANGE (a) INTERVAL (1000) (   
    PARTITION p1 VALUES LESS THAN (1000)) ONLINE;

You could convert indexes too, adding:

update indexes (index_name [local/global]);

db<>fiddle demo

Beacuse your table non-partitioned you have two options:

1. Export data, drop table, create new patitioned table, import data.
2. Use split then exchange partition method. https://oracle-base.com/articles/misc/partitioning-an-existing-table-using-exchange-partition

Also, if you want new partition per month read about SET INTERVAL. For example:

CREATE TABLE tst
   (col_date DATE)
 PARTITION BY RANGE (col_date) INTERVAL (NUMTOYMINTERVAL(1, 'MONTH'))
(PARTITION col_date_min VALUES LESS THAN (TO_DATE('2010-01-01', 'YYYY-MM-DD')));