My kids ALWAYS get slivers during the summer, as they run around outside and explore, and they ALWAYS scream and fight us as we try to get them out - or they used to, until we figured out this secret to getting them out painlessly.
Step 1: Orajel
Just squeeze one tiny drop of Orajel medicated teething gel for babies on the sliver or right where it is sore. Wait 10-15 minutes and the teething remedy acts as a local anesthetic and numbs the area. Then you can use a sanitized pin or needle and tweezers to dig it out and the person with the sliver won't feel a thing!