You have to write at 225 words a minute in order to graduate, but some people are able to write at speeds of 300+ words a minute. If you look at the keyboard, the machine is separated into two halves. On the left half there are only 9 keys, but each letter of the alphabet can be written with those 9 keys because it's context sensitive. The letter "t" by itself would be the letter t, but if it's next to a "k", it might become the letter d. You mentioned that we can knock out certain letters such as c, and that's indeed what is done with stenography. The word "car" is written "kar". There are sometimes conflicts, like "sell" and "cell", so you still need a way to write a c, but that's the gist of it.
Worth mentioning is that there are only 4 vowel keys on the machine (the vowels are the keys that are on the bottom), but you can write a lot of different sounds with these four keys. A, O, E, and U are the vowels that are on there, and if you press one of those keys individually, you'd write a short vowel of that key. If you wanted to write a short I, you'd press E and U together. You would write long vowel sounds by combining different vowels together. So for example, if you wanted to write a long e sound, you'd write aoe, long U sound would be aou, long a sound would be ai (or aeu depending on how you look at it), long o is oe, and long i is all the vowels together at once.
It can be hard to read what you've written if you're not extremely good at it. The word dime, for example, you would see as "TKAOEUPL". There are a few different theories out there, and even if everyone learns the same theory, everyone puts their own little spin on it, so if you wanted to read what someone else wrote, it might be tough.
This is the layout of the keyboard if anyone is interested (http://dmc122011.delmar.edu/ba/crtrgallery/images/steno_keyb...)