If you want, you can separate the lower joints in order to individually clean those parts of the instrument, but most of the time this isn’t necessary.
Remember to wash your cloth on occasion. A dirty cloth will put germs and saliva back onto the reed.
Specialized swabs can be bought online or at music supply stores.
At least once a month but preferably once a week, deep clean the mouthpiece.
A typical dish soap is also capable of cleaning the mouthpiece in cool or warm water.
A baby toothbrush can also be used to remove limescale.
You can leave the mouthpiece to dry on the paper towel or cloth to make sure all the moisture is gone.
