Here's what elf ears look like, slideshow courtesy of Instructables.com. What you're seeing are pictures of a girl who's had her ears cut and re-sewn to give them that slightly pointed shape not unlike Spock from Star Trek or Orlando Bloom's Legolas from the Lord of the Rings movies. The girl is Kimberleigh Roseblade and her body artist is Russ Foxx, both from Vancouver, Canada. Kimberleigh is 24 years old and will now have elf ears for the rest of her life, baring corrective plastic surgery.
Chances are this will become like split tongues: a highly-desirable, teenage "must-have" and a body modification that the Powers-That-Be attempt to ban and/or legally restrict as a medical procedure. This is not something that anyone should do at home, on a whim or without lots and lots of forethought and research. This is one of those body mods where there's no turning back and where you need to find someone who knows what they're doing if you truly decide that such a modification is appropriate for you and your lifestyle.
Just looking at the pictures, it would appear the upper crest of the ear and ear rim are cut and then sutured to reshape them, with a butterfly bandage offering some more shaping and support to the healing tissues. This part of the ear is cartilage, a flexible but thick body tissue (your nose is also mostly cartilage). Dangers with cartilage are that if an infection occurred, the ear might not heal together into the pointed shape, leaving you with a slit and deformed upper ear. Blood circulation is not as good as with soft tissue, so absolute meticulous aftercare would be crucial to help ensure the best healing possible.