To fart quietly, release the gas slowly by tightening up your abdominal muscles, and also you could make a masking noise like a cough or a chair movement when you need to fart.
Walking and shifting your weight while seated when farting can also make for a different exist path for the gas.
When farting, inhale deeply then tense your abs, by slowly inhale and tighten your abdominal muscles to control the release of gas.
Then instead of letting the gas or fart out all at once, release it slowly and gradually to minimize the noise.
You could also wad some toilet paper up if possible and jam it in your anus to create a filter for the sound of the fart.
What makes a fart loud is a high volume of gas that is forced out through your tight anal sphincter, which causes the muscles to vibrate and create sound waves.
This sound is similar to a brass instrument, with it's volume and pitch changing based on the amount of gas, the force with which it's expelled, the size of your anal opening and the tightness of your sphincter.
When your anal sphincter muscles are tensed, they create a narrower opening and the gas pushing through the tight passage causes more vibration and a louder fart sound.
Fart noises are basically caused by vibrations as gas escapes your anus.
To let out the biggest fart, lay down flat and then pull your legs towards your head.
Then relax your rectum and let the air seep in slowly and then wait until you feel a fart forming your gut and then let it out.