A splinter or sliver is a foreign object that has stuck or jammed its way under your skin. These foreign objects penetrate only superficially, but due to their proximity to nerve endings, they can cause wincing pain. Some slivers are made from glass or plastic, which can be transparent or otherwise very difficult to see. Unfortunately, the only way to remove these is by relying on feel, however momentarily uncomfortable that may be.
Clean the area around the sliver, using wipes, hydrogen peroxide, rubbing alcohol or some other sanitizer. When wiping, wipe in the direction that you want to remove the sliver, which is the opposite direction from where the sliver entered. Pushing in on the sliver can be very painful and cause bleeding.
Feel for the length of the sliver with some object, like a cotton swab. When you are confident of the exact location of the sliver, take a sterilized razor or craft knife and make a superficial cut on the top of the sliver. This should expose the large end of the sliver.
Use tweezers if you think you can reasonably feel for the splinters end without breaking it off, or place tape over the most painful spot on the sliver. In both cases, pull slowly in the opposite direction of the way the sliver penetrated. Clean off the area and bandage it when the sliver is extracted.