Use 'look for' when describing an active attempt to find something, often involving physical or mental effort. They were looking for the hidden treasure in the attic.
Pro Tip 2/3
Extended Time
'Look for' conveys that the search may take time, not usually something found immediately. She spent hours looking for the perfect dress.
Pro Tip 3/3
Not Literal
Sometimes 'look for' is used figuratively, meaning to seek something abstract or not physically present. He's looking for happiness after a tough year.