I work in a company from which I resigned 5 months ago, and then rejoined. Here is the situation: 3 months after I rejoin, I receive a better offer. Now how do I handle this situation? How do I tell this to my boss?
As @Dukeling hints in their comments, you may need to examine why you always find greener grass on the other side of the fence because continually hopping jobs will become a problem for you, if it hasn't already (I'm sure any references from your current employer will be 'interesting' considering...)
But there's nothing special you need to do when giving your notice, except maybe look apologetic and try extra hard to keep things professional if you get a lot of pushback from your boss.
I suspect that you will be burning bridges with your current employer and possibly senior staff that work there if you do leave, but the only way around that is to not quit and if you're sure the new job is the right one for you then that's not really an option either is it?
If you have any desire to continue to work at this company or to return again to work at this company - you don't. Presumably, you knew your own market rate and thought this was the best option to return to a second time, when you came back 3 months ago. And, as a returning employee, you knew much more about what you would be getting into than you did the first time through. I have a hard time believing (and I bet your management will too) that the new offer is so much mind-bogglingly better that you would be crazy not to try it. So... if you give notice this time, be prepared to leave for good.
With that said, if you have really gotten the offer of a lifetime, then give notice, give at least the standard notice, and be short, sweet and polite. At this point, don't expect a counter offer - you literally just renegotiated your salary - it's too soon to reasonably try again. Send a thank you on your last day and head out.