You know that you are not actually Cleaning your clarinet. What you are doing is Drying it. Clarinets do not like moisture. Pads will deteriorate sooner if they are wet and the clarinet will get moldy after a while. Especially, its not a good idea to place a wet clarinet into a closed case. It can not breath or dry out. The best way to dry a clarinet is to let it air dry. If you have a safe place to put it, then just leave the lid of the case open and let the clarinet dry overnight. Many times you do not have the opportunity to do this like when you are at school, so you must use a swab. Pull through swabs come in different styles but they do the same thing, They remove the moisture from the instrument.
Pull-through swabs have a weight on a string that is dropped through the instrument and when it comes out the other side you simply pull the swab through the instrument several times. Simply just remove the Mouthpiece after playing. Let the weight drop through from the Barrel end to the Bell end.
Pull gently because the Swab has to clear two metal tubes in the inside of the clarinet. If you pull too hard and too fast the Swab can get stuck and tear.
Hold on to the weight at the Bell end and pull the swab through the instrument.