If the egg hatches (which it will for our characters) the dragon will come out, touch it's head to your hand.  There will be a flash of light and you'll feel pain in your hand, and you'll find a glowing silver mark in your palm.  Then, as per instructions, you'll pick up your dragon, and go off to the tables on the right and take a seat.  You'll also be able to name your dragon too.  Also, I recommend reading the books, so you can better understand what's going on.  Google Play store has all four books as a bundle deal for like $20.