I hope to contact a professor in the grad school i want to work under him. What are some tips and things I should pay attention to in my email? I will go to a grad school this summer. I don't want to make mistakes in that email as I really work to work under him. I wrote an email before I applied and he said we can talk. 
What should I write now?
I think the main thing is showing a genuine interest in their work. I think the main way of demonstrating this is actually knowing of their work. Good ways of doing this is 1) reading some of their recent and most impactful papers and 2) talking with people in the lab about what the current research directions are. The other thing I would strongly encourage is not to commit to working with them unless you are absolutely sure you want them as a doctoral adviser.