Try this, changing the * to the columns you require (p.size, m.medium_name etc):
SELECT *
FROM paintings AS p
INNER JOIN painting_medium AS pm
ON p.pid = pm.pid
INNER JOIN medium_options mo
ON pm.moid = mo.moid
INNER JOIN medium m
ON mo.medium_id = m.medium_id
So your first line would be along the lines of:
SELECT p.category AS Category
,mo.medium_option AS Size
,m.medium_name AS Material
FROM paintings AS p
etc