The job of Assistant Head is not a catchall, or "whatever the head doesn't want to do." Outline, publically, specific middle-management duties for your Assistant Head, so she or he doesn't get showered with the fatal "other duties as assigned." Not only will your Assistant Head know the job, the assistant's position will be clear to the entire school community.
Accountability to clear responsibilities will give the Assistant Head a tangible reason for existing, and defines the assistant's scope of responsibility. You avoid the assistant being mistaken as the day-to-day decision maker; constituents will be less likely approach the assistant on any topic at any given time.
The assistant should report directly to you, but may supervise other administrators as your deputy. The Assistant Head only takes over when the head is absent. Period. Establish when the transfer of power goes into effect, and have a process to communicate this transfer to the school.
When the assistant is acting as head, the assistant is temporary management team leader. The assistant needs to make sure the rest of the team maintains regular operations.
Remember, you as the head remain ultimately responsible for all aspects of the school's operations—including the duties of the Assistant Head. Do not abdicate—stay in touch, in the loop with the information flow. Lead your management team meetings, get in the classrooms, be seen in the hallways. Make sure the assistant fills you in so you are privy to all aspects of the issues at hand.
Make the assistant aware of the full picture of all the issues and how they affect all constituent groups. Afterall, the assistant must be able to fill in for you. And when informing the assistant, make it clear whether or not this is a time for feedback or just a briefing.
You can assign the assistant special duties, as an ad hoc head for special projects or tasks, for example. If you do, you need to specify what resources he/she can rely on, outline how often you want updates, what you expect when the project is complete, the ultimate outcome of the project, and the level of confidentiality you expect.
Your Assistant Head should be someone you can rely on as your sounding board when necessary, as your aide to help free up your schedule, and as your replacement when you cannot be there. By properly defining your assistant's duties and providing quality training, your assistant will enhance your management team's effectiveness.