Imagine that your sister has been blind since birth, and lives cloistered in a monastery in Tibet. You describe a problem you are having with your husband and his mother ever since your recent marriage. She listens patiently and then carefully helps you sort through all the emotions and events that have allowed the problem to build to the point of explosion. Although she has never "seen" your new husband, talked to him or had any direct contact with him, she has asked you many carefully questions and noted your responses.
She then guides you to what is at the root of the problem, and helps you come up with a plan of action to resolve the problem.
This analogy is not perfect, but it illustrates what "science" does. Over decades, and even centuries, scientists make observations of how things react that they may not be able to see. They mix chemicals, heat them up and measure the changes and results. Over time they construct "models" or ideas about how "something they can't see" might be structured. The model is tested, and if the model explains most of what we see, and it allows us to predict what will happen, then we use the model until a better one comes along.
Today our model of the atoms looks like the image shown below.

Scientists care more about predicting the behavior of things in the universe than they care about having a model that mimics "reality," what ever that may be.
Optional Historical Stuff
Democritus, an ancient greek philosopher, is credited with elaborating a full theory of the atom from the thinking of philosophers as they contemplated "What is the nature of matter?" They speculated that by dividing a bar of gold, silver or other piece of matter, you would ultimately get to the smallest possible piece; and that smallest piece was termed an "atom." Melissus of Samos, in attempting to explain all the different kinds of matter, wrote "But if there are Many, they must each have the character of the One." Melissus would not be surprised to find out that modern atomic theory assumes there are gold atoms, silver atoms, and essentially a different kind of atom for every different kind of matter in the periodic chart.
Some images of the overall shape of atoms or molecules can be made with a scanning tunneling microscope. Click the following to see an image of a layer of iodine atoms and a DNA molecule. These images are from Hans Christian Von Bayer's Taming the atom, Random House. The iodine image is compliments of Fran Heyl and the DNA is IBM Research and Science Magazine.