First working only 3 years for a Fortune 500 company is NOT a good sign. Why only 3 years? I have personally interviewed a lot of personnel during my career so far and the first question I would ask you if I were to interview you is "Why didn't you last? Are you a job hopper?"
Having said that, you can follow the below generic guidelines to resign professionally and leave the least amount of hatred behind:
- Don't tell anyone of your colleagues about your intentions prior to resigning
- Tell your manager FACE TO FACE that you are resigning. Don't accept a counter offer, don't say bad things about the company/your manager/colleagues (just don't badmouth anyone), don't say where you're heading or how much you will be getting, keep your temper even if your manager lost his, politely ask about a severance package (if you're entitled to). Always keep in mind during this conversation that you will need your manager for reference.
- Once you told your manager and agreed on the terms, you have to make your resignation official, as in a printed resignation letter. Make sure you don't email your resignation, have it printed and signed (unless of course you are reporting to someone overseas, in this case you have no other option than to send an email/fax), and then followup with a "goodbye" email, sent to your managers and your colleagues as well. Your resignation letter should be very brief, it should include to whom the letter it's addressed to, the date, and a very short paragraph telling your manager about your resignation, and praising him and the company (saying that you had a lot of fun during your job, hoping for the paths to cross again, wishing the company good luck, etc...). Your goodbye email can include GOOD feelings, nostalgia, etc... and should be emailed to everyone you've worked with in the company.
- Have a face to face 5 minute chat with any potential reference: As a project manager, your only asset is how many successful projects you have managed, and the only people who can confirm this are your references. Make sure they are happy with you when you leave. You may think that you can skip this step if you already secured a job somewhere else, but remember that your next job might not be as secure as you had hoped for, and you might be looking for another job pretty soon, so you WILL need those references.
You might be asked to leave the premises immediately so be prepared for this. You might also be asked to surrender any of your current belongings to the company (such as the company's car, company's credit cards, etc...) the moment you make your resignation public.
Now about your case (you're saying that you're working on an important project with no replacement), my advice to you is not to resign at the moment. Keep working on the project until you're done. If you can't do this (the other offer is waiting or the project will take a long time), then discuss your resignation with your manager and tell him that you are willing to stay a maximum of x months or until a replacement is found, whichever comes first. This will alleviate you from the moral impact of your resignation in this case.