Silencing an alarm is a procedure, and the order of the steps is the safety part. Establish there is no fire, then silence, then find out what caused it, then reset. Doing it in any other order, or doing it by pulling something out, is how buildings end up unprotected without anybody deciding to make them unprotected.
In a building with a panel
Confirm from the panel which zone or device operated and send somebody to check it before doing anything else. Once you are satisfied there is no fire, use the panel key to enable the controls and press silence, which stops the sounders while leaving the alarm condition displayed. Investigate, then press reset, which returns the system to normal. Record the whole event in the log book including the cause.
Silence is not reset
Silencing stops the noise and keeps the alarm condition visible, which is what you want while somebody is still checking. Resetting clears it and loses the display on a conventional panel. Resetting first is the common mistake, because the noise is what people want to stop, and it throws away the only information about which device operated.
A domestic alarm that will not stop
Most domestic alarms have a hush button that silences a nuisance activation for a few minutes while the air clears. Use that. Do not remove the battery, do not bag the alarm and do not take it off the ceiling, because all three are decisions to live without detection that nobody ever revisits. If it will not stop with the hush and there is no smoke, it is telling you the alarm needs replacing.
The chirp that is not an alarm
A single chirp every minute or so is a low battery or an end of life warning. The manual says which pattern is which. On a replaceable battery unit, change the battery. On a sealed unit, or where the chirping continues after a new battery, the alarm has reached the end of its life and needs replacing whole. Neither is fixed by pressing anything.
Questions people ask about how to turn fire alarm off
How do I silence a fire alarm panel?
Confirm there is no fire, use the panel key to enable the controls, and press silence. Investigate the cause, then reset. Record the event and the cause in the log book.
Why does resetting before investigating matter?
On a conventional panel the zone indication is lost on reset, so you throw away the only clue to what operated. On an addressable panel it stays in the event log, but the habit is still worth keeping.
Can I take the battery out of a smoke alarm that keeps sounding?
No. Use the hush button and find the cause. Removing the battery is a decision to live without detection, and it is almost never reversed as quickly as intended.