The classic sign is a door that stops a few inches off the ground and won't budge, with the opener motor straining or clicking as it tries to pull weight it can't lift alone. Sometimes it's quieter than that - a door that feels noticeably heavier to lift by hand than it did a year ago, which usually means the spring is losing tension gradually rather than snapping outright.
A loud bang from the garage, especially in cold weather, is often the spring itself letting go. If you hear that, don't run the opener again - a broken spring can let the door drop fast, and running it further risks the cable or the opener's drive gear next.