I just went through this process with my last employer 3 weeks ago. I just finished week one at the new employer and it is great. Here is what I did.
Gave 2 weeks notice, I told my boss this opportunity was too good to pass up. It was something I really wanted to do.
Offered to do whatever was needed over the next two weeks to help with the transition. (Mostly documentation for the new guy and closing outstanding projects.)
Recommended that they expand a current contract they have with a service provider to help fill some of my roles while they look for a new employee.
I kept the exit interview and discussions with other employees professional and did not complain about the problems of the current job. Really no reason at this point to make a big stink on the way out, I don't like to burn brides un-necessarily.
I hope this helps.
Good luck with the new job!