I've seen dozen of videos on how to replace the ignition switch but in every video, they have the old key. I lost my key so how do I get the old cylinder out?

 

You will need to drill out the tumblers so you can turn it to on
Then it will come out by pressing the pin
On position is the only way it will come out (only spot where the pin has a cavity to recess into)
It's easy to drill because it is pot metal except for the tumblers
Good luck

 

Well I drilled out the cylinder starting with a fairly small bit and gradually up to a 1/2" bit. The drill depth was deeper than the length of the key. The cylinder still will not turn. What am I doing wrong?

 

The drill will force some of the tumblers up into their respective holes or slots
Just drill bigger or fight them out so you can turn what's left of the barrel
The pin should be able to be pushed in at any point now. (after turning it clockwise a bit)
Good luck

 

Well I've royally screwed up now. I got the lock cylinder out but then realized that I drilled too far in and destroyed the little slot mechanism that the cylinder fits into to actuate the ignition. I've been online looking for replacement parts but can't find a decent diagram with Ford part numbers.

 

That little geared wheel behind the snap ring?
You can get one from the junkyard
It has to be clocked in there correctly for the ignition switch to have all its positions
Hopefully the snap ring is still there in its groove, and you do not need a tilt hosing or mass jacket
All that stuff can be had at the junkyard cheap
Good luck