How to use the rate of change of frequency equation to calculate frequency drop in a grid based on lost generation
If the equations can be used to calculate frequency drop from a lost load, can they also be used to calculate how the frequency would increase if a load was added? Is it a matter of a positive, or negative sign in front of the delta P?

First of all, when load (demand) is added, frequency goes down and vice versa. Having that said, yes, you can use the equation for both cases. The inertia itself will change slightly because added/dropped load has inertia itself, but you can neglect it.

How does MW*s/MVA (inertia constant) on the right side of the equation &quot;cancel&quot; to just seconds? Why do you have MW over the rating of the machine MVA? I think this is meant to be a &quot;ratio&quot;?

Ratio is &quot;unitless&quot;. MW and MVA are essentially the same units. You use one or another to make it clear what physical parameter you are talking about.

And explain how a change of rate in frequency (HZ/s) on the left side can equal a change in power per second (MW/s) on the right side.

Well, in fact they do not say that \$\frac{df}{dt}\$ is in Hz/s. I suppose they just left out some constants in the left part of the equation.
You may start with a swing equation of a synchronous machine
$$
\frac{2H}{\omega_s}\frac{d^2\delta}{dt^2}=P_m-P_e
$$
where Pm, Pe are mechanical and electrical power in p.u.; \$\delta\$ is load angle in radians and \$\omega_s\$ is angular velocity in radian/s.
Mechanical power is provided by turbines and electrical power is drawn by loads.
Then substitute \$ f=\frac{1}{2\pi}\frac{d\delta}{dt}; f_s=\frac{\omega_s}{2\pi}\$ and switch from p.u. powers to MW and you can get the equation
$$
\frac{S_{rated}}{f_s}\frac{df}{dt}=\frac{\Delta P}{2H}
$$
where \$\Delta P\$ is power imbalance caused either by load change or by generation tripping; \$S_{rated}\$ total rated power of all synchronous machines under consideration.

I am hoping someone can give me an example calculation on how much the frequency would drop based on how much generation was lost using the aforementioned equation.

Things are a bit more complex. Let's suppose you have load drop in your system. Synchronous machines start to accelerate and frequency starts rising according to the swing equation above. At the same time load starts to increase because of rising frequency (this is called load response; in the National Grid presentation they state load response 2% per Hz). After some time frequency goes out of turbine governor's deadband and they start to reduce power generation; governors may have
different droop - the rate at which they change power with change of frequency; typical droop is 5%. This stops frequency rising. After some more time power station target power output is adjusted and frequency returns to the normal value.
In general, you would need more or less precise power system model and power system simulation software to calculate frequency change. If you try to use one single equation for the whole system you in effect represent the whole system as one equivalent machine; this is not very precise.
What you may try to estimate is the frequency at which rising/falling is stopped at first stage, that is when new balance is reached. The balance is reached due to load response and governor action. Thus
$$
\Delta P = \frac{k_{LR}}{100}P_L\Delta f + \frac{100}{d}P_{rated}\frac{\Delta f}{f_s}
$$
where \$k_{LR}\$ is load response in percents; d - droop in percents; \$P_L\$ total load power; \$P_{rated}\$ total rated power of generators in work; positive \$\Delta P\$ corresponds to load loss, negative - generation loss.
You can solve this equation for frequency deviation. It would be good to test the equation on real data and adjust equivalent droop and load response accordingly.