壊れる and 壊す: break down or cause loss of function
Distinguish a machine or object ceasing to work from a cause damaging it. Accidents and natural forces can be causes, so the contrast does not by itself establish intent.
An object breaks or a cause damages it
壊れる describes a machine or object losing its function or failing to hold its form. 旅行中にカメラが壊れました。 marks the camera that stopped working with が.
壊す presents a cause damaging an object. 弟がリモコンを壊しました。 marks the damaged remote with を. The sentence alone does not establish that the brother did it deliberately.
Accidents and natural forces can be causes
無理にふたを開けて、留め具を壊してしまいました。 says that someone forced a lid open and damaged the fastener. てしまいました can express regret about the accident.
A natural force can also be the subject of 壊す, as in 強い風が庭の傘を壊しました。 Using a transitive verb does not require a human acting intentionally.
Connect the broken state to the repaired result
事務所のエアコンが壊れています。 describes an air conditioner that is currently out of order. It can present the continuing result of a breakdown, rather than only an action happening at that moment.
After a repair, one can say 修理の人がエアコンを直したので、今は使えます。 壊れる presents the change that caused the problem, and 直す presents the action that restored normal operation.
Quick check: To state only that an umbrella broke because of strong wind, which is correct, 傘が壊れました or 傘を壊れました?
Show the answer and why
傘が壊れました is correct. The umbrella that broke is the subject of 壊れる, so it takes が. To name the cause as the subject, say 強い風が傘を壊しました。