I don't know if they teach typing in school these days, in the same way we used to be taught handwriting (and hopefully children still are!). If they don't they definitely should, because it's not something you just pick up, as is evident from the zillions of two-finger typists.
As a PhD student I type a lot, either emails and web browsing or actual writing of text documents. And I spend a fair amount of my leisure time typing too, doing things like write this blog. Furthermore, I (and many other people) need to type for my job - when I used to work for a talking newspaper, much of the day was spent typing articles to record later.
I can type quite adequately for my purposes. I just tested my speed and I got 59wpm, which is just in the range of 'average professional typist' (50-80wpm) according to Wikipedia. But this wasn't always the case: when I started working for the talking newspaper I was another two-finger typist. I was actually really quick, and Wikipedia tells me that such typists can reach 60-70wpm in bursts, but I was always aware that I could be better, and it would be faster and more comfortable.
One day, I can't really remember why, I googled free online typing course and just picked one, and have never looked back. It took me about two hours to complete the course, and it was probably the most useful two hours I've ever spent. I urge you to do the same if you're like me. Do the course as slow as you like - I wanted to get maximum gains in as little time as possible, but I could have been more thorough. But do it, because the time it saves you and the difference it makes to your writing is astonishing.
It's not just the increase in speed and accuracy, either. If you can touch-type, you don't have to be looking at the keyboard the whole time so you can focus on what you're actually writing. And secondly, if you can type quickly and without real conscious effort, you can concentrate on the content instead of thinking about where the next key is.