Not much... The commonly used atom model does deceptively look like a planetary system, but it is a gross simplyfication so your imagination can get a better grasp of it.
The electrons don't have nicely organised orbital paths around the core. They zoom around it in quite chaotic patterns, at ludicrous speeds. The atomic forces holding the whole thing together are much stronger than gravity (proportionally) but don't reach very far, so we don't feel them outside the atomic level.
Also, how the atom effectively looks is depending on the material. Metals, for example, don't have any organised pattern of electrons around their cores at all. It's more like a giant cloud with electrons whizzing from atom to atom through the whole bloody molecule. Shoot an electron in on one side, and another one flies out the other end. That's why metals are so good conductors.
So no, imagining atoms as miniature planetary systems is missing reality by quite a stretch.
