Formal charge and net charge
Net charge is the sum of all formal charges of the atoms in a molecule. Net charge is the charge of the molecule.

Formal charge is the charge of an atom in a molecule. Formal charge varies when you look at resonance structure. See this post of the nitrate resonance structures. It can be obtained through:

\begin{equation}
Formal\ charge\ =\ Valence\ electrons\ -\ no\ bonding\ electrons\ -\ \frac{bonding\ electrons}{2}\quad\quad\quad\quad\quad\text{(Eq. 1)}
\end{equation}

Example: I take the example given previously with $\ce{NO3^{-}}$, in order to give a complete answer to the present post. 

So, Having in mind the rules to draw the Lewis Structure:


Operations


Sum the valence electrons of all atoms. When the system is an anion, an electron is added. When the system is a cation, an electron is subtracted.
Sum the 'octet-electron duet' of all atoms.
Subtract step 2 of 1. Results corresponds to shared or bonding electrons.
Subtract step 3 of 1. Result corresponds to the nonbonding electrons.

Indications


Assigns two electrons to each bond.
If electrons remain from step 3. Add them in pairs creating double or triple bonds. Having in mind the duplet/octet rule.
The obtained electrons from step 4. Add them in pairs to the more electronegative atoms.
Calculate the formal charge of each atom.



Then:


Operations


$$valence\ electrons\ \cdot\ number\ atoms\ of\ \ce{N}\ +\ valence\ electrons\ \cdot\ number\ of\ \ce{O}\ +\ anion\ condition $$ Then $$5\cdot 1+6\cdot 3+1=24$$
$$octet\ of\ \ce{N}\ \cdot\ number\ atoms\ of\ \ce{N}\ +\ octet\ of\ \ce{O}\ \ \cdot\ number\ of\ \ce{O} $$ Then $$8\cdot 1+8\cdot 3=32$$
$$32-24=8$$
$$24-8=16$$


Indications




After doing the first three steps, you will get:

 (Source: Stackexchange)

Now, taken equation 1 to nitrogen:

$$Formal\ charge\ of\ \ce{N} =\ 5\ -\ 0\ -\ \frac{8}{2}\ =\ +1$$

Now, taken equation 1 to oxygen bonded to nitrogen through single bond:

$$Formal\ charge\ of\ \ce{O} =\ 6\ -\ 6\ -\ \frac{2}{2}\ =\ -1$$

Now, taken equation 1 to oxygen bonded to nitrogen through double bond:

$$Formal\ charge\ of\ \ce{O} =\ 6\ -\ 4\ -\ \frac{4}{2}\ =\ 0$$

Therefore

Net charge of $\ce{NO3^-}$ is the sum of all formal charge of the atoms in the molecule equals to -1