How do I inform my immediate boss/supervisor about the offer?
I usually inform the immediate supervisor early in the day, after the morning status meeting. Beforehand, I try to have all my personal possessions out of the office: some companies (especially in the finance industry) will escort you to the door as soon as you give notice, others will want you to work through your notice period.
I also try to have a written resignation letter handy. Based on past experience, resignation letters should be 3 and only 3 sentences.
- I will be resigning my position at $company.
- My last date of work will be $date.
- My address is $address.
3.14 Sign and date the letter.
Reason for sentence 1: it is a resignation letter, there needs to be zero misunderstanding about what is going on. It needs to be in writing as I've worked for bosses who deny that the person quitting was quitting so as to screw with them starting elsewhere.
Reason for sentence 2: I've worked for places that have backdated resignation letters and claimed you quit today - not in 2 weeks. Consequently, you may be expecting a paycheck that you'll never recieve. This is also why you date it with "today's" date when you sign it.
Reason for sentence 3: Many people move, and if you need COBRA benefits, or 401k paperwork, there have been places I've worked at where they would deliberately and maliciously send your paperwork to an old address so that you cannot reply in the mandated 30 day period (because either it was still tied up in the post office's change of address system, or if that expired, returned to sender).
Never ever add stuff to your resignation letter about why you are leaving. It is none of their business. If they ask, answer verbally, but never in any sort of writing.
Should I try to negotiate about a matching offer, or should I terminate the contract outright?
If they ask, let them bring it up. All the places I've left, I've left for large raises that they cannot and would not match.
How do I inform the team? Do I tell them early on, or right as I'm leaving?
This is a cultural issue that depends on your workplace's culture. Some want to inform everyone affected as soon as possible, others want you gone with no one knowing you have gone.
One book that has a useful chapter on leaving is called Engineering Your Retirement. It is aimed at technical people, and it gives plenty of advice (and equations) to help determine how much is enough to save for retirement. The checklist and advice at the beginning of chapter 8 is what you should keep in mind whenever you depart any employer (due to quitting or getting laid off).