How to delete records in one table based on the values in another table?

use DELETE with subquery:

DELETE FROM table1 WHERE table1.cm_id IN (SELECT table2.um_id FROM table2 WHERE order_num>=518 and order_num<=520)

I prefer this way

delete from table1
using table1, table2
where table1.cm_id = table2.um_id
and table2.order_num >= 518
and table2.order_num <= 520;

DELETE table1
FROM   table1 INNER JOIN table2 ON table1.cm_id = table2.um_id
AND    (table2.order_num BETWEEN 518 AND 520)

--OR

DELETE 
FROM  table1
USING table1 INNER JOIN table2 ON table1.cm_id = table2.um_id
WHERE   (table2.order_num BETWEEN 518 AND 520)

EDIT:

There was a duplicate FROM and query has been changed as per Andriy M comments.

delete 
from table1
where cm_id IN (select um_id from table2 where order_num between 518 and 520)