Where does the extra electron come from in the Lewis Dot Electron structure of say for example nitrate ion?
Unfortunately your Lewis structure for the nitrate ion, $\ce{NO3-}$, is wrong. You did not include any charges and as it is an ion there is at least one. Let's first have a look at how an ion may be formed and then hopefully you see, that there is no mystery at all about it.

Take for example ordinary table salt, which has the chemical formula $\ce{NaCl}$. If you dissolve it in water the lattice will be broken and the ions will by hydrated and are now able to move more freely.
$$\ce{NaCl_{(s)} -&gt; Na+{}_{(aq)} + Cl- {}_{(aq)}}$$

The same happens when you dissolve potassium nitrate, which releases the nitrate ion:
$$\ce{KNO3_{(s)} -&gt; K+{}_{(aq)} + NO3- {}_{(aq)}}$$
Here you can see, that the nitrate ion has an extra electron which it has taken from the potassium. See ionic bonding for more information.

For the Lewis structure of the nitrate ion you first have to count all the valence electrons of the involved atoms:
\begin{array}{lclr}
1 &amp;\times &amp;\ce{N} &amp; 5\\
3 &amp;\times &amp;\ce{O} &amp; 6\\
1 &amp;\times &amp;\text{charge} &amp; 1\\\hline
  &amp;       &amp;              &amp; 24\\
\end{array}

In the Lewis structure you have to distribute 24 electrons in a fashion, that you do not violate the rule of two, which is better known as the octet rule. Therefore your structure may include a nitrogen oxygen double bond, a positive formal charge on nitrogen and a negative formal charge at each of the singly bound oxygens.
Another representation is that all oxygens are singly bound and therefore the nitrogen has a $+2$ formal charge and each of the oxygens has a negative formal charge. The problem with this structure is that nitrogen does not have a full octet. Nevertheless, it is a strong contributor to the actual electronic structure. The bonding situation is much more complicated than can be expressed through a Lewis structure. The concept of resonance structures has to at least be included. Better in this case would be molecular orbital theory and or valence bond theory. The molecule itself is a y-aromatic system, the charge is delocalised through the extensive $\pi$ system. The blue structure is an attempt of showing this feature.