Why are atoms larger going down a group
Atoms get larger because the higher the energy level, the more orbitals it has and the further away from the nucleus those orbitals are. Also, more electrons are interfering with the attraction that the nucleus has on the highest energy electrons [shielding].
Why do atoms get smaller going from left to right across the table.
Atoms get smaller because there is an increase in the effective nuclear charge [more protons attracting more electrons) so the highest energy level get pulled in closer to the nucleus.