The Basics
You can create tasks by emailing x@mail.asana.com. Asana will create a new task, assigned to you, in your default workspace. The name of the task will be the email subject, and the body of the email will become the notes.
Email a task into a specific project
Each project has an email address of the form x+ProjectID@mail.asana.com. The project ID is the first long number in the URL for a project. You can read the full instructions here.
Assign, Attach Files, and add Followers over email
All of these actions work for new tasks and when replying to an existing task.
To assign a task to someone else, put them as the only person in the To: field (you can add the asana email here or in CC/BCC). You won't be able to assign the task to another person if you are emailing x@mail.asana.com (since this creates the task in YOUR assigned task view). You can create and assign a task in another project using the x+projectid@mail.asana.com syntax.
To add someone as a follower, put them in the CC: field
Attachments to emails will survive and will attach to the task created.
Complete Tasks
To complete a task, reply "Complete" as the first line of your reply to an email notification for a single task update

Email Support