It doesn't seem like swabbing out a clarinet would be such an important topic, but trust me: It certainly is important because your swab can super easily get stuck inside the upper joint of your clarinet and no one wants that. So please watch my video below that shows the proper way to take care of your clarinet.
Video of me correctly swabbing out a clarinet and cleaning the mouthpiece, etc:
Photo of inside of upper joint - see the bit that protrudes inside the clarinet joint? That's the bit that can get snagged on your swab. --------------------------->
Photos of swabs that are NOT your friends = these are bad news:
Link and photos of a swab that IS your friend = this kind of swab is GOOD news: