how to make a design on a card that stands out like a bubble?

Answer 1

Are you making the card on the computer or by hand? If on the computer using Publisher software you can use the 3D effect and shadow the image.

If by hand, you could use puff paint. Without knowing what you are going to do, I cannot give you an adequate answer.

Answer 2

if it is a greeting card, or similar stock paper material, iron it with an iron and steam it. while it is hot, and very moist, press it over an object (rubber ball?) and push another rounded obect over it. Then...let it dry in the sun.