My first aid book 'First Aid Made Easy' which I used for my refresher training in February says:
If a splinter is embedded deeply, difficult to remove or on a joint, lave it in place and follow the advice for embedded objects. Other splinters can be removed as follows;
-Carefully clean area warm soapy water
- Use pair of tweezers, grip splinter close to skin as possible and gently pull it out at same angle it entered
- Gently squeeze around wound to encourage a little bleeding. Wash wound again, then dry and cover with dressing
- Seek medical advice to ensure casualty's tetanus is up to date

For info it's the same for paediactric first aid too.

Hope this helps :-)