Some splinters can get very deep and the only real course of action is to use a needle. Before using a needle you should sterilize it. The simplest way to sterilize a needle is to hold lit over an open flame for a second. A match of candle will do.
It can be difficult to hold a sewing needle stable while trying to remove a splinter. To give yourself something easier to hold onto, push the blunt end of the needle into a cork from a bottle of wine until it is very secure. Now you can hold the needle with a sort of handle, making manipulations much easier. Moreover, this needle is a lot easier to store on a shelf in the bathroom, without it getting lost, falling on the carpet.
Using a safety pin can be better as it is also easier to hold.