Autocorrect will not get you far... Did you ever make the same spelling mistake over and over? When that happens to me I quickly choose the correct spelling, just to make the same mistake again.
So - to actually practice typing the right spelling or grammar corrections, I've created Correcto - a small chrome extension which will present an input box for you to practice typing the correct spelling of the mistakes you're making.
It works automatically on Gmail and Docs, and across the web you can choose "Retype with Correcto" from the context menu (right click) for each mistake instead of automatically correcting it.
You can try it here: