For the past half a year or so, I've had an entry-level part-time position outside my field of choice. Despite the nature of the position, the lack of benefits, and the menial work, I've more or less enjoyed my time there, and I've always been on good terms with my boss and coworkers.
Recently, I discovered a training program in my desired field that sounded perfect. I applied, with full intention of resigning my current position if I was accepted, but never mentioned it for fear of being rejected from there (for the longest time, they held me at conditionally accepted) and replaced from the job that I had.
Today, I received a confirmation email from the training program saying I'm officially in. The problem is that it has a fixed starting date, conflicts irreconcilably with my current work schedule, and gives me only enough time for a one-week notice rather than the usual two-week notice.
How should I resign from my current position? What should I tell my boss? Should I specifically apologize for the lack of notice? I've always felt very replaceable and I doubt they'd have any trouble at all finding someone else, but I'm on good terms and I'd like to leave on good terms.