Atoms are composed of nuetrons (neutral), protons (positive), and electrons (negative). If you think of the charges like they are on a number scale, count towards the middle from each charge. Let's say you have an atom with 4 electrons and 4 protons. Draw or mentally think of a number line.
-4. -3. -2. -1. 0. 1. 2. 3. 4
Move toward the middle of the line, recalling that opposit charges will cancel out- like when two people push against each other, and yet they don't move that much.
-2. -1 0. 1. 2
-1. 0. 1
0
The end result of all these opposites canceling out is zero. That is how the charged particles can be in an atom that is neutral in charge.