What is the best way to ease the pain in a toddler's finger injury?

Buddy tape/ice&meds. You should take your toddler to see a board certified orthopaedic surgeon, for x-rays, evaluation and treatment. For now, you can tape the injured finger to an adjacent one and try otc children's tylenol/motrin. Ice is also helpful, but can be difficult to use on a toddler.