To access most your cards, login to your account and tap "Post Box" at the bottom of the screen. You will then be able to tap through the menu on the left to get to your upcoming events, photo galleries, sent, and received cards, as well as your PAPER Orders.
To access any unsent or drafted events, instead tap "Drafts" at the bottom of the screen. You'll be able to tap between online and PAPER drafts.
To access all of your cards, tap the account menu at the top left of the screen, then tap "Post Box." You'll then be able to tap between your upcoming events, photo galleries, sent and received cards, online and PAPER drafts, and your PAPER orders.
Unlike on iPhone, your Drafts will appear in the same place as the rest of your cards.