Stick it horizontally. From this point on, working on the beak is easier if you attach it to the bulk of the bird. Gently push the top of the beak down. This is probably the only resemblance the bird would ever bear to an eagle, so you have every reason to do it. This is what the aspiring bird looks like with his modified beak.
Next step consists of separating the upper jaw from the lower one.
This is when you first use the safety pin. Drive it into the beak where the curved part starts and pull to the cheeks. Don't touch the part that is bent down though - this is where the jaws remain joined. It's safer - in case what you make turns out to be a really hungry bird. Use the safety pin again to widen the distance between the jaws.