Well for starters, pick some symbols that represent your family and heritage. For example, if you're Australian, maybe a Kangaroo, or the Sydney Opera House, or if you're French, the Eifel Tower, and a beret, etc... You're going to want four images, and they don't all have to relate to your nationality, you could do other things relating to your family, like if you all use computers a lot or something, you could use a picture of a computer, etc... Now you'll want to start with some sort of shield, how that looks is up to you, but make it nice and big, at least fill a page with it, and then divide it into four quadrants, and put 1 picture in each quadrant.
Now I don't know the assignment, but you could do either just a picture on paper, or make a real coat of arms, but if it's just the picture, then you're done. If you're making a real coat of arms, then when you do the shield, you'll want to not put the pictures on yet, and cut out the shield you draw, and then glue it to a piece of wood, and have an adult cut it out for you. From there, paint the pictures onto it.