Always start by washing and drying your hands. Dirty hands will wreak havoc on the baby's delicate and sensitive skin so make sure you wash all the germs away prior to every changing. Settle the baby down on a changing table, or any soft, warm, clean, and dry area. You can even place your baby down on a blanketed floor. Unlatch the baby's old diaper and use its corners to wipe away any excess poop, but don't remove the dirty diaper just yet.
Babies are funny like that.
Gently grasp the baby's ankles together with one hand and lift her bottom off the table. Use baby wipes or a wet cloth to wipe the baby's genitals clean. If the baby is a girl, make sure you wipe her from front to back to minimize the chances of infection. Some people would now apply baby powder or some other kind of talc to the baby's bottom. If you're babysitting, check with the parents beforehand to see what they usually do.