How do you treat a broken toe? How do doctors decide when a broken toe should be left to heal on its own and when it needs medical intervention?

Crooked? . If the toe is crooked it might need surgery to fix it. See a podiatrist.
Broken . Broken toes are almost always appropriately treated without surgery, at least at first. There are certain fracture patterns or specific location where a foot bone can break that will not heal readily without a surgery for example. In general though, toe fractures heal well with as little as a hard soled shoe for a few weeks to splint the fracture and protect it while it heals. If the toe that is broken is significantly displaced or angulated because of the fracture, it can be easily realigned by someone comfortable doing so. This could be an orthopaedist or an emergency doctor in some cases. If there is a skin laceration associated with the fracture, or if the bone has come through the skin, this would also be a reason to seek medical attention.