What are the formal charges in #"O"_3# (ozone)?

A formal charge is equal to the number of valence electrons of an atom MINUS the number of electrons assigned to an atom.

Consider the resonance structures for #"O"_3#.

Oxygen has #6# valence electrons. Look at the top left oxygen atom. It has two lone pairs (#4# electrons) and a double bond (#2# electrons).

Even though a double bond contains #4# electrons total and is counted as such when seeing that oxygen's octet is filled, #2# electrons belong to each oxygen and they are shared among the two.

Let's examine the top resonance structure:

Left: #6# valence #-6# assigned #=color(blue)(0# formal charge
Center #6# valence #-5# assigned #=color(blue)(1# formal charge
Right: #6# valence #-7# assigned #=color(blue)(-1)# formal charge

Notice that even though the atoms have varying formal charges, the overall charge of #"O"_3# is the sum of the formal charges in the molecule: #0+1+(-1)=0#.

Ions' formal charge sums are #!=0#.