I have put in a couple lawns at different houses. I am by no stretch an expert, but I can tell you what we did. Cost-wise the $5 is likely just the sod. You may need to rent equipment to prep the yard, but there is really nothing crazy you have to do to prep.
We had very rocky soil at both homes, and in one of them we just put sod on a small-ish section in the front yard and, as the soil compact with watering, we ended up with a lumpy lawn. It was weird to walk on and to sit on. So when we did the back yard, which was much larger, we rented a tiller and tilled it to remove the bigger rocks. We dug them out and used them for surrounding the yard in the flower areas and such, looked good. This was when we had the sprinklers installed. Then we borrowed a grading rake from my friend and graded the yard so it sloped away from the house. Even just a very slight slope is preferred. We just eyeballed it really. Then we watered the dirt pretty heavy and let it dry and settle for a couple of weeks, graded it again, then watered and let it settle again. Not sure if this part is necessary for a lawn, but I know you should do this when putting down concrete to minimize cracking, so I figured for a flat smooth lawn it couldn't hurt. I got some nice topsoil from a neighbor who had extra after putting in some flower beds and a garden area and we spread that over the dirt in an even, but thin, layer. Again, don't know if that is necessary but it seemed to help the lawn take and grow better than the front yard that had none.
The next day the sod came and we laid it down in a cross-hatch/parquet pattern that minimizes lines and grooves in the lawn. Then we watered it solidly every other day (long watering less frequently is generally better than short watering a lot, at least that is what our lawn guy told us). After about 3-4 weeks, to let the lawn get set, we hit it with fertilizer/weed killer. The finished lawn was flat and smooth as a golf green. We have put in 2 other lawns since then, and I helped a neighbor, using this same method and it worked great.
I am sure you don't have to go to the trouble of tilling and getting a grading rake. You could probably remove large stones with a shovel and rake it relatively smooth with a regular rake and I am sure it would be fine.
Not sure if that is what you were looking for, but there you go.