You can use a correlated sub query as below. This assumes there will be exactly one matching value returned. It will raise an error if more than one matching value is returned or set the field to null if zero are returned. If that last behaviour isn't desirable you will need a where
clause.
UPDATE table1
SET field1 = (SELECT DISTINCT table2.ValueColumn
FROM table2
WHERE table2.JoinColumn = table1.JoinColumn)
Edit
To review records with 0 or more than 1 matches you could use
SELECT table1.JoinColumn, COUNT(DISTINCT table2.ValueColumn)
FROM table1
LEFT JOIN table2
ON table2.JoinColumn = table1.JoinColumn
GROUP BY table1.JoinColumn
HAVING COUNT(DISTINCT table2.ValueColumn) <> 1