How do I tell my boss I'm leaving? (nicely)?

I would say it depends on how close you are to your boss. It's best to do it in person. I would suggest beginning by thanking him/her for his/her guidance over however long you've been there. Then, tell him that you've accepted a new position, and give him/her plenty of notice to find a replacement for you.

There's no single way to do it but I'm sure if anyone knew how to tell your boss it would be you. Possibly think of what you might want to hear if you were the boss. Ultimately, it's entirely up to you and I hope that your instincts help you to make the best decision for you. Best wishes.

Something like "I have really enjoyed my time with this company and am grateful for the opportunities I have enjoyed here and now I would like to make next step in my work life and take new opportunities, so it is time for me to leave with a regret as I will miss my colleagues... etc."

Just be honest. You don't have to give more information than you're comfortable giving. Be professional, allow for a decent amount of notice and tell your boss. Employees come and go all of the time and no one is bound to stay somewhere where they are no longer challenged or when they find better/alternative opportunities. If you're concerned your employer won't understand that, it's really not because you have an issue, it's because the employer has an issue. A good employer knows that things change and they encourage employees who decide to move on to other things. Good luck!

Ask to meet with the boss, explain that you feel it is time to leave and explain what you will be doing next (new job, moving, going to school, taking some time to work on health issues). Thank them for the time spent in their employment. Do not unload issues at this point. If the boss asks if anything negative happened, answer honestly, but consider how much you share and why you're sharing it. It is important to not burn bridges and to come away on a positive note with a good reference...you will need it again in the future.

You could write him a letter saying that you quit and why. You could give him a call explaining that your leaving the job or if you feel confident enough, Just simply go up to him, ask to have a private chat with him, tell him that your quitting the job but the polite thing you could do is giving him the reason why, Just telling your boss that you quit without reasoning is kind of a slap in the face so it's really just best that you explain your reasoning.

I'm assuming by leaving, you mean quitting. A nice way to tell you boss that you are leaving depends largely on how your boss considers your resignation. I would definitely have this meeting outside the workplace, maybe over lunch in a restaurant. You could start by thanking him for his mentorship and support, and tell him how great it has been working with him and how much you have grown professionally and (maybe) as a person. You could then talk a bit about how you have found yourself seeking newer challenges, and that you think a new job will help you feel more satisfied and fulfilled. Always end with promising to keep in touch and do not burn bridges. On the other hand, if you do not have a good relationship, a formal setting with an HR personnel might be a better way to go about it.

Thank them for the opportunities you have had with the company but firmly let them know that you need to seek out new learnings and adventures

You can google some templates that help you figure out how to word it in a professional manner. E-mail is always helpful, but if you have to say it in person, write a script for yourself based on research, practice, and there you go. Just remember to remain professional and even if they were awful, thank them for the opportunity they gave you.

By wording it in a way that is grateful. "Thank you for this opportunity, I'ver really grown since working here. That's why I regret to inform you that I will be leaving in two weeks" Reflecting back to your time at the job and how this change will positively impact your future.