Fast typing is not fast fingers. A single keystroke takes about the same time for everyone and practice barely changes it. Three other things do change, and the rest of the course is built around those three.
First, movements overlap. When the next letter belongs to the other hand or another finger, that finger can already be on its way while the previous one is still pressing. Two movements run partly at the same time, and the time you gain comes from that overlap. This is why alternating words run fast and same-finger sequences run slow: in the latter there is nothing to overlap.
Second, learned sequences. An experienced typist does not think about single letters. The hand produces frequent letter pairs and whole short words as one learned movement, much as a musician does not think about single notes. That is why letter pairs and frequent words give you more than hammering individual letters: what you learn is not a faster press but a sequence you no longer have to assemble.
Third, where you look. Every time the eyes travel from the screen to the keyboard and back, time is lost and so is your place. That is the whole point of touch typing: the key does not have to be searched for. With the hands on the home row, every letter is always the same distance away and the hand knows it without looking.
Mistakes cost more than slowness. Fixing a mistake takes several times longer than typing the letter correctly, because it has to be noticed, deleted and the place found again. Accuracy is therefore a precondition of speed, not its opposite.
What to expect. At first speed grows quickly, then it sits still for a long while, and that is normal: the hand is busy learning sequences the clock cannot show yet. The gains come from short regular sessions rather than one long evening. And the biggest gains go to whoever keeps to the proper finger assignment even where a wrong finger would be quicker right now.
If you are starting from nothing, begin at the home row and work down the list in order. If you already type and want to get faster, the most useful ones are same-finger sequences, letter pairs and frequent words. The rest of the lessons are listed below.