80% of people feel nothing at all. The other 20% feel a "tiny pinch". The word to concentrate on here is "TINY". The needle is removed a split second after the piercing is made and thrown into a medical sharps bin immediately to reduce the danger of sharps injuries to both you and your piercer. This leaves the tube, or cannula, behind. This cannula is cut in half to allow removal of the clamps. This also ensures that it CANNOT BE REUSED. Once the clamps are removed, the cannula is used to guide the jewellery through the piercing. The cannula is then thrown into a medical sharps bin for incineration.
To ensure that you are at your most relaxed at the time of your piercing, some piercers may need to use one of a number of special relaxation techniques ranging from just wiggling your toes to deep relaxation or light hypnotherapy depending how anxious you are at the time. It's a good idea to be honest about how you feel so that they can tailor the procedure to your needs.