As for how you can obtain one, straight from the FAQ:
Q: What is the Amabie Promo Card and how do I get one?
A: Similar to Omamori charms in Japan that are used to promote good health and ward off Sickness, Amabie is a Japanese spirit said to repel the plague by showing copies of itself to people.
While supplies last, every time a Duelist registers for any event other than the Main Event, they will receive one (1) copy of Amabie in addition to any other commensurate prizing for that event.

NOTE: This is taken from the US/Canada FAQ. There is no info on the official site at this moment for other TCG regions.
Source.