Once you decide on the type of lip piercing you want, ask your piercer if you have a choice between a lip stud and a lip ring or if the type of lip piercing you're interested in requires a certain type of lip piercing jewelry. If opting for lip studs, you'll probably actually get labret studs, which have a flat disc on the back that's less likely to irritate your gums or other parts of your mouth than the inner curve of a ring may. If you find that a traditional metal labret stud is uncomfortable or are worried about it damaging your gums, you can get a bioplastic flexible labret stud to wear as a lip ring that has a softer backing. Those backings can be easily cut down with a dermal punch to get a disc that's just the right size for your mouth.
Once you've chosen the type of lip piercing you want and have selected your jewelry, your piercer will sterilize the jewelry by autoclaving it. S/he will then clean and mark the area to be pierced. If you're happy with the placement, the next step is to insert an appropriately-sized piercing needle, followed by your new jewelry.