A little late with a reply, but I am a civil engineer and deal with subdivision grading plans on a daily basis.
The first thing to do is call the engineering department at your city and ask them their policy on lot-to-lot drainage. If it is allowed, you have to fix the problem yourself. If it is not, then you need to get a copy of the subdivision grading plan that was done by a professional engineer and see how your neighbors and your yards are supposed to drain. This can be purchased from the city for a couple of bucks, maybe free. If the grading plan shows his yard to drain away from yours, then you have a case.
The city building inspection department is responsible for assuring that the builder retained the drainage pattern approved on the grading plan when he built the house. Changing the drainage pattern can be a major deal depending on the circumstances. You should take pictures, shown them to someone in building inspection and demand they take action. The neighbor will have to redo his entire yard and probably build a retaining wall on the back property line to raise his ground elevation to make water flow to the front of his yard.
If this is your problem only (lot to lot drainage is allowed)then you need to grade a swale (shallow ditch) from a high point in the middle of your back property line and have one run over to the right side property line and one to the left side property line and both run right out to the front.
If lot to lot drainage is allowed or it's not but they can't fix the problem for some reason, there needs to be a drainage easement granted by you and your left and right neighbors to the guy behind you all. This should be noted on the final plat of the subdivision, also obtained from engineering, if lot to lot is allowed. If it's not, then you can make them pay for the work to build the swales around your yard or whatever you want in exchange for granting them the easement.
I hope I wasn't too technical. Good luck!
Q
Flagstone with grass
Q