Dab on vegetable oil
Pat some vegetable oil on the affected area and wait a moment for it to be absorbed into the puncture.
Then gently remove the splinter with tweezers.
The oil softens the skin and helps the splinter slide out.
Try glue
If you have a small splinter that is too small to get with tweezers, try using white glue or facial mask glue.
Pour a thin layer of glue or gel over the skin and let it dry. Then peel the dried glue/mask off taking the splinter with it.
This works well for wood splinters, fibreglass fragments and cactus spines, thorns etc.