OK, things have progressed through the offer stage and you are ready to resign. Depending upon how you manage the process, this can either be a smooth transition or a "sticky wicket."
If you have already discussed your dissatisfaction with your supervisor on earlier occasions, there should be little surprise. If you have never discussed leaving with your supervisor, he/she will likely be surprised and faced with two conflicting emotions ... anger that you are leaving and a desire to hold on to you with a counter offer. (for more details see counter offers)
The first rule of thumb is to make sure you have a firm offer in hand. All testing should be finished, background checks completed, and all contingencies have been lifted.
The next step is the actual resignation. It is always best to resign in person, face to face. If this is not possible, then you need to do it over the phone with your supervisor. It is not recommended that you resign by fax or email as that is considered unprofessional.
Depending upon how well you know your boss, the conversation should be unemotional, direct and concise. For example:
"I know this may come as a surprise to you but after a number of months of evaluating my career with (the company), I have decided to accept another position."
OR .... If your concerns have been previously discussed.......
"I know this will not be a huge surprise based on our previous conversations, but after a number of months of consideration, I have decided to accept another position with _____________."
"I appreciate (all you have done for me) OR (all that I have learned during my time with the company). My new position begins immediately; however, I want to give you as much notice as is needed for a smooth transition."
It is standard practice that one offers two week's notice. It is unprofessional to offer less and it is equally unprofessional that the company would ask for more. However, there may be a large account or order that is pending, and you might agree to stay involved with that one project for a bit longer.
In discussing the resignation, it is important not to blame your existing firm for the change but to focus on the new opportunity that you have in hand.
Many companies will ask you to put your resignation in writing, so you should be prepared to do so. The best rule here is to keep it short, simple and factual, yet you need to be gracious for the opportunity that you were provided.