set a column with value from different table

Say that you have Table A:
  • username
  • email
And Table B:
  • item_id
  • username
You want to add email to table B where the value taken from table A. After adding a column on Table B, this query can be used:
SET email = tableA.Email
FROM tableA
WHERE tableB.username = tableA.username
AND IS DISTINCT FROM; -- optional, see below
The final WHERE clause prevents updates that wouldn't change anything - which is practically always a good idea (almost full cost but no gain, exotic exceptions apply). If both old and new value are guaranteed to be NOT NULL, simplify to:
AND <>