Visit the Grammarly for MS Word and Office page to download the plug-in. Run the .exe and follow the installation instructions (you might want to install only the Word add-on if you don't use Microsoft Outlook for email). You'll be prompted to log in to your Grammarly account, or you can skip this step and log in from inside Word.
After a successful install, you'll see a Grammarly button in Word to the far right!
To initiate a Grammarly check, just click the button. You'll be able to see the different options available across the top of Word. You can tell Grammarly what kind of essay you're working on, and enable or disable checks for things like spelling, sentence structure, vocabulary enhancement, and even plagiarism.
Any issues that Grammarly finds will be underlined inside your document, and the suggested change will be recommended in the side panel to the right.
To learn more about the grammar rule behind the suggestions, just click the the little arrow icon to expand the short lesson.
To accept the change, click on the green (to the right of the -> arrow), corrected word/phrase.
Grammarly's browser extension support page has links to the appropriate pages where you'll be able to download and install Grammarly to use in your browser. You'll gain a little green button to trigger Grammarly checks, but it will also check your writing in the background (no need to click).
This is especially useful if you have any classes that require you to post to D2L, or (of course) anywhere else online where you're typing out content to share.