SELECT *
FROM my_table
WHERE 
   col_1 IN (select id from something) AND
   col_2 IN (select id from something_else)

##</code><code>##

SELECT *
FROM my_table
INNER JOIN (select col_1 from something) A USING (col_1)
INNER JOIN (select col_2 from something_else) B USING (col_2)