In the Modern Periodic Table, there are 18 vertical columns known as Groups and 7 horizontal rows known as Periods.
As we move down the group, the electrostatic attraction between the nucleus and the outer-most electron decreases due to increase in the distance between them. This happens because, on moving down the group, a new shell is added. So the valence electron can be easily lost by the element. As we know, metallic character is characterized by the ease of loss of an electron, thereby, metallic character increases on moving down a group in the Modern Periodic Table.
When we move across a period, the number of electrons in the same shell increases. This leads to greater electrostatic attraction between the nucleus and the outer-most electron. This increased attraction pulls the outer-most electron closer to the nucleus, thereby decreasing the atomic size.