Before you jump in and invest a lot of labor and money in material, make sure the bumpy lawn isn't just due to the difference between turf crowns and bare soil. You state that the lawn is sparse, do you mean that it is patchy with "clumps" of grass interspersed about the lawn? If so, your problem may cure itself once you have a uniform coverage of grass.

It is truly bumpy, there are not clumps of grass in areas. It is more or so grassy in most areas and spare in areas of less sunlight or where there were a build-up of leaves and the grass died over the winter.

There have been a number of good posts on "yard leveling". Best to use sharp sand, the type used by masons for mixing mortar. I don't recommend mixing anything into the sand, particularly not topsoil or compost. If you feel obligated to add something, you could add one shovel of dry peat moss for every 20 of sand. Mow the lawn short, distribute sand over an area as best you can with wheelbarrows or buckets without making large piles. Use a drag or push brooms and the back of garden rakes to evenly distribute the sand off the high spots into the lower spots and bring the grass blades up. Water well when finished.
Alternatives include using a vertical slit seeder to help smooth out the lawn or plug aeration over a number of years.
Good luck.

Edit: I would strongly recommend that you start with a small area with bags of sand to get an idea of how it is done and the amount of material needed before you commit to a load of sand from a garden center or other supplier. Always visit to make sure of what you are getting before you order.

This post was edited by yardtractor1 on Thu, May 29, 14 at 14:42

Thank you. We have decided to use sand here and there until we get it where we want it to be. Buying a couple bags at a time. We still want to use the lawn while this is going on, so we won't be doing it all-in-one. I think it will work for us.

The reason you don't use topsoil when leveling is the clods you always have. If you can get topsoil which has been ground to powder, then fine. Clods roll around under the drag or screed and ruin the leveling effect.