Blueprints are pre-made coaster designs that you can assign to a placed coaster. They are cards that can drop in Weekly Coaster Challenge rewards, or in packs bought in the shop, like the Coaster pack - but they are very rare!
To craft them, you need the full list of cards that compose the design of the coaster: the full base set of the coaster type, and any special insert, train or station modifiers. You can see what cards are needed in the build menu.
To assign them, select a placed coaster. Tap on the crane button, then on the Blueprint button. From there you can drag a valid blueprint on the scene to assign it and see the result. Exit the menu to validate or cancel your choice.