You could think of the communication as having three parts:
(1) Introduce yourself and your interest. Minimal details about yourself, possibly just your educational background. A sentence or two about your interest in the subject, and how you came across the professor/their work.
(2) Convey your work in the area of mutual interest, in a sentence or two.
(3) Request them for guidance in how to improve grammar (or whatever specific area you're looking for help in). Convey where you have already searched (effort taken is generally appreciated), and what you still have problems with. Finally, mention that if they are interested, you would be happy to share samples of your work with them.
The shorter the email, the more likely they are to read fully and respond.