Keep schedules in mind and don't over-promise on response time. The student should be aware that many professionals use e-mail frequently and may receive dozens of emails daily. This is especially true when returning from a vacation or business trip. The weekly contact doesn't have to be lengthy. A quick note just to stay in touch might be all that's necessary.
Consistency is the key.
Setting the parameters of the relationship early and keeping it professional will avoid embarrassment and complications later. As with any relationship, honesty is the key. Both sides must feel comfortable suggesting topics and expressing their opinions. If the student and mentor live close to each other, in-person meetings can be arranged. Monthly dinners at local restaurants might be an alternative to emails.