There are a couple ways to check your spelling in Google mail.
If you spell something incorrectly, it will be underlined in red.
You would then just right click on the misspelled word and select the correct spelling.
Click on the triangle by the trash can in the bottom right corner.
Select "Check spelling"
The misspelled words will be highlighted.
Click on the misspelled word and select the correct spelling.
Spell Check in the Chrome Browser
The first is the simplest. If you are in Google Chrome, their is an automatic spell check in the browser.If you spell something incorrectly, it will be underlined in red.
You would then just right click on the misspelled word and select the correct spelling.
Spell Check in GMail
You can also spell check in the compose window.Click on the triangle by the trash can in the bottom right corner.
Select "Check spelling"
The misspelled words will be highlighted.
Click on the misspelled word and select the correct spelling.