This is what the builder looks like when you first visit the page. You need to select the number of sets you own and the click hide sets in the upper right corner.
After you've done that once it should look like this when you visit it next time. Hovering your cursor over the spell will display it. There are 16 slots, each holds a separate spellbook. Spellbooks will persist across sessions if you use the same browser/computer. You can export/import, but the format (at this point) is not compatible with other builders so it's only good to move your books around and use this spellbook builder.
If you still have issues try a different (and up to date) browser. If that doesn't help feel free to PM a screenshot and I'll look into it.
What card would you like to add? A few promos or a bunch of cards (for example adding Academy)?