It's hard to tell a boss that you like, but generally the longer lead-time is useful for them, so don't delay trying to find the “right” way to tell them. If they're sending you a formal offer, I'd wait till I had that (just in case they changed their mind), but once you had it, I'd type up a nice but simple resignation letter (important to have it in writing for HR). Then, depending on the relationship you have with your boss, either just walk to their door and say “Hey, got a minute?” or shoot them an email and say “I need to meet with you briefly today if possible, when would be a good time?” The discussion only has to last 1 or 2 minutes, so don't feel bad about just dropping in on your boss, presuming the work environment is one that would permit that. Your boss may expand it to a 1-hour discussion of the status of various projects, but they can expand it or keep it short at their preference based on what else they have going on.
IMPORTANT: Resignation letters should always be fairly generic. If you've had issues, don't put it in your resignation letter. If you've had a great time, you can put it in your cover letter somewhat, but still keep it brief and to the point. Your resignation letter is part of your formal, permanent HR record, so isn't the place for a 6-page essay on why you've loved your job and boss or all the issues at the company. The first might be appropriate in a private letter to your boss, or a formal commendation; the second in a formal complaint. But, the resignation letter isn't the place for either.
Here's how I've done my past few job resignations:
In-college job (they knew I was seeking an accounting job): IIRC, I emailed my manager and told him I needed to talk with him and my supervisor once he got in (he'd call on clients first and get to the office around 11 or 12 usually). It was the first job I'd had that I loved the people I worked with, so my female boss and I both teared up and/or started crying while I resigned, and my male manager had to be the one to be responsible and go through the official things that needed to be talked over (when the last day would be etc.) while trying to keep us composed…then the three of us walked out of our office to where the rest of the staff was and he said “Ladies (he was the only guy haha), as you know, Lilla has recently graduated. She's found a job in accounting and will be leaving us in a couple weeks. We wish her all the best.” Then some of the others teared up. Darn emotional womens… Glad I've learned to be less of one at work now. 😉
First accounting job: I formally accepted my new job on the 1st day of my vacation. Brought with me my resignation letter for my current job (at a micro-firm, only other employee was the owner/boss); on the way back from accepting the new job, I stopped by my current office, let myself in the back door, walked into my boss's office, told him I'd found a new job and gave him my resignation letter. He said he'd figured this was coming – with me working on my CPA, he figured I'd be leaving for something more exciting. Actually left for an Accounting Clerk job just to move to private, but oh well.
Second accounting job: My boss and I had discussed my future within the company, and we both understood that the company didn't offer what I was looking for. She'd told me when she interviewed me that she hoped this could be a good springboard position for me, so she knew I wouldn't be there long. So, when we'd begun to discuss the future, she'd asked that I let her know when I had a serious prospect…so, during our monthly status meeting, I'd told her I had a final interview for a position later that week. Therefore, when I walked into her office (probably emailed her first to make sure she was free) the following week and told her I'd gotten the job, it wasn't a surprise to anyone. After we discussed a few items, and I appropriately thanked her for all the opportunities that she'd provided (I was hired as a Clerk, allowed to do the work of several positions higher, and learned a LOT), she walked out to the room with everyone's cubicles and announced my official departure, and told them who she wanted to have learn what from me, since we all had segregated duties and there were things people would need to learn before I left.
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