Check the alarm system for your septic tank, if yours has one. Some alarms emit a light to warn that a septic pump has failed. Others emit a sound like a buzzer. Your alarm might be on a pole by the septic tank. If you're unsure where your alarm is, contact your septic system technician. An alarm may also indicate that the pump is simply unplugged, rather than broken.
Look at your yard near the leach field. If you see or smell sewage rising to the surface in the yard, this could indicate a failed septic pump.
Run water in all of your plumbing fixtures in your home. Make a note if any of them drain sluggishly or refuse to drain altogether. This also indicates a failed septic pump. Depending on the severity of the situation, you may also notice sewage backing up into your home.