I've taught this trick to several of my friends and family and it hasn't failed yet to turn a 16-20wpm typer into a much more accurate 60+wpm within only a few painless sessions.
Once you learn the home row and can type without looking, even if barely, unplug the keyboard and turn on the tv. Turn on the closed captioning and just chill and watch tv and try to type as much as you can of what they're saying. If they pause for a long time type whatever is last on the closed captioning over and over till new words are said. While you can't keep up you just type as much as you can.
You can do it for hours without getting fatigued cus you're entertained by the tv and not focused on the typing. It quickly breaks the habit of looking at the keyboard because you want to watch the tv and not the keys and since you're going by natural speech your brain learns much more quickly to process the keys pushing you to higher speeds and also giving you much higher accuracy.
my sister and brother in law just recently failed a very important typing test that they needed to get a job and only had 5 days to get up to 35 wpm to retake the test and they were both ridiculously bad typers who could only peck out 14 wpm. I told them about my trick and within only two, two hour sessions of watching tv they could type 40wpm with over 90% accuracy so they easily passed their test.
I also think teaching people how to IM does wonders in the same way.
