First, Address him or her in a friendly way. Don't iclude sir/ma'am because you exactly don't know who is the client is.
Then, Include about your self in very short sentences. (in brief). may be 2-3 short sentences.
Include about your experience and skills. in which software you use/expert
then try to mention, that you got the idea of the client request, or you can combine the skills you expertise with the request of the client. (make more attention to this!!) also its important to have strong portfolio. so you can include the shortened link of your portfolio.
Add your opinion about the work and show how you can improve the clients' idea. What are your deliverables. And ask a question for client inside your description.
At last, let the buyers to contact you
You can get an idea with my below mentioned sample.
If we think some client asking for business logo, with minimal and modern style. He mentioned his business details( assume, he has a food business and name is Fast cook) and he mentioned he needs to add the letters of the business to logo. you can make the proposal like this.