This, too, is a great question--one of the most important issues in raising orphans.
I like to use a warm, moist cotton ball and make gentle circles around the kitten's genitals. Gentle is the operative word here. Don't use any more pressure than you would if you touched a baby's eyelid.
My fosters prefer my husband's technique over mine. He blows warm breath in the kitten's face--like the queen would do. (I'm simply not coordinated enough to do both at the same time.) He also uses a paper towel instead of cotton.
I'm not sure if you're talking pee or poop, but a constipated kitten might be dehydrated.
If you're having problems getting a kitten to go, try stimulating after dinner. If that doesn't work--a trip to the vet's in order. Any vet or vet tech should be able to tell you if there's a problem with the kitten or if it's your technique. They can most likely give you a lesson in Weeing the Kitten.