The AHDI Book of Style has a lot of grammar information specific to transcription, and most companies use that as their grammar and style source for transcription.
For general grammar information, I would suggest getting a good grammar book and studying it and also using it for a reference when you are transcribing. I bought the Gregg Reference Manual used on Amazon.com
for about $10 a few years ago. There is also a workbook to go with it that you can purchase (new and used copies also). Just search for "Gregg reference manual" to see them.
Of course, there are other good books also, but that happens to be the one that I have and I found it to be excellent. Before I got that I used an old high school English textbook (like 25 years old) that I bought at a yard sale for $1!
Also, try googling "grammar website" and you will see a lot of sites that would help as well!