If you have a stock Android device (running Android Lollipop or Marshmallow), go to Settings -> Language & input -> Google Keyboard. There, you'll find a "Text correction" sub-menu from where you can turn off auto correct with just a tap on the corresponding toggle.
If you don't have a stock Android device, you'll first need to locate the Google Keyboard (assuming it's installed on your phone), and open it. Once you do that, you'll see the "Text correction" sub-menu that we mentioned above, and, after accessing it, you can, once again, disable auto correct with one tap. Needless to say, if you want to, you can turn the feature on again at any time.
In both cases (stock, or non-stock Android), you may want to leave all the other Text correction options enabled, as they won't automatically do anything - they'll just show word suggestions, and it's you who chooses to use them or not.
Folks who don't have the Google Keyboard app, but want to try it, can download it for free from Google Play (see the download link at the end of this article). The app works on devices running Android 4.0 or newer.
P.S.: This short tutorial was made on a Nexus 5X running stock Android 6.0.1 Marshmallow. Things may look different on your device.
download: Google Keyboard