If you have a splinter in your toe, can I pop it out?

Maybe. If it is fresh and you can see the point of entry you may be able to squeeze it so you can grab it with a tweezer and remove it.
Usually. Most people will wash the wound, soak in epsom salts and use tweezers to remove splinters. If you cannot do this then you should see your doctor, particularly if there is increasing redness, swelling or pain.