I patched and filled several areas this fall, in New England, with great success. First, I removed all the debris; someone had turned wire fencing under the ground from a garden of the original owner, about 8 years ago, along with wooden posts. Every time I started to rake the existing soil smooth, my rake caught something else. I finally just dug it all up by hand, and then smoothed it out.
In area where there was existing grass that I was going to cover, I burned it with a propane blow torch; the kind that attaches to a grill tank. I then covered it with a mixture of top soil, peat moss, grass seed, and starter fertilizer; all together. I would mix the top soil and peat in a wheelbarrow, and then add the proper proportions of seed and fertilizer. I put down about an inch or two of that and raked it lightly to smooth it out. I did not tamp it down. I watered it every day to keep it moist, and with the sunny an cool weather we had in September, the grass all came up in a week; and I mowed it twice before it stopped growing for the season. This was not the first time I had used this approach, but it turned out better than ever before because of the cooperative weather. I actually did that previous garden area in early October, and the weather was a bit cooler. That area sprouted in about 10 days, but never got to reach full height; yet.
The backyard of this house we bought 2 years ago must have been filled when the house was built, as it has settled more since we moved in. I filled some of it to correct that, but some of those areas, 1 to 2 feet in diameter, continue to sink. So, I just sprinkle soil over them without completely covering the grass. and let the grass do whatever it need to to adjust.