You should first learn the keys assigned to each finger. Then try typing tests over random letters so that your fingers get used pressing the right keys. It may take some time to achieve this if you actually don't use all your fingers when typing. If you notice any finger pressing another key that it is not supposed to press, do it again with the right finger -as a punishment. Once you can use all your fingers (maybe only 9, I only press spacebar with the left thumb) you are ready to try typing quotes, at least once a day. Remember being focused at the accuracy: you will reach speed without noticing it if you first focus on accuracy! And then, in three or four months you will become a really good typer, probably reaching speeds over 100 wpm! And a last advice: try not to look at the keyboard.

@sebas3552 did an amazing job at explaining exactly what to do and I agree with him 100%. I also really think memorizing the keyboard is really important, and should be your priority, if you haven't already memorized it. I think a great way to do this is to have a live keyboard moniter on your screen so that if you get stuck and don't know where a key is, you can easily see it- whilst training yourself to not look at the keyboard. Pretty weird. But it works, for me at least.
I also think that typing a lot is a good idea, but make sure you're taking breaks. I found myself in a period of time where I wasn't improving at all, so I took a break of 2-3 weeks and right after I improved about 10 WPM!

Good luck with everything. You'll improve soon enough ^_^

What you can do to learn to type faster is talk with people online. I learned to speed up my typing by playing games w/ text chat & atleast for me, using IRC. Typically most people these days use discord / slack communities to do real-time online communication w/ text chat. This will speed you up tremendously with your standard phrases. If you learn to write code, you'll get used to typing a lot of the other keys. I would get a keyboard without a number key-pad.

Just for some information. I learned to type @ 14 in HS. I wasn't faster than 30wpm until I started to use my computer at home regularly outside of school. Same year went from 30wpm to 55-60wpm. These days as an adult, I type around 90-120wpm. Special symbols & un-common words always trip me up when I type on speed test sites.