The first tip is to always brush your teeth before you start playing; we can imagine the air that we put into the instrument like a river flowing, and that, where it encounters obstacles or detours, settles what it carries; then we must ensure that our river composed of air and saliva is as cleare as possible. Personally I prefer to let the damp mouthpiece rather than always pass the rag, since moisture remained not create damage in contrast, continues his removal which can vary the inner chamber of the mouthpiece.
Always use the least abrasive strips (suede, silk ...) and avoid using the clarinet strip if it is too large.
Never place the mouthpiece plan on abrasive surfaces, even on a simple sheet of paper and always tuck with reed and narrow band just as well as to protect the most delicate part.
More or less every 15 days at room temperature water slide in the mouthpiece and with a cotton swab wet remove any residue; if you persist you can be diluted in a pint of water a drop of mild soap and repeat the treatment; Never use hot water and aggressive products.
It is useful to periodically run a reorganization by the craftsman, like a coupon, to be programmed more or less every year, even though the weather varies greatly from case to case, depending on the hours you play, the type of band that we use and how care we preserve it.
I often fix the reed without even loosen the clamp, and this is surely detrimental for our mouthpiece; if you did it once, nothing happens, but if repeated three or four times every day we play, in a month already become more than a hundred, and in a year ...
The reed crawling firmly on the mouthpiece tends to unbalance and even if you seem to remain unchanged over time, in reality it is not so: the friction causes of subtle changes in the near to which, however, the clarinetist eventually adapt. The result is that these added together small changes from year to year, change the mouthpiece and, consequently, our way of playing. I think it is for this reason that those who play the same mouthpiece for a long time, generally make much more effort to change it and to find a new one that satisfies.