Start at the lower part of the slope. Remove soil with the bulldozer as you climb the slope and deposit the soil at the lowest end of the slope. Continue relocating soil in this way, removing it from the higher spots and depositing it at the low ends, until the backyard is reasonably flat.
Spray the soil with a garden hose to keep the dust levels down.
Use the 2-by-4 scrap wood to level the soil. Drag the wood along the top of the soil to smooth out the rough spots by having a person holding each end. Think of this smoothing of the soil as the way you might frost a cake.
Check the soil with a carpenter's level placed on top of the 2 by 4. Rake the soil so it slants away from any buildings. Any rainfall should run away from the house to prevent flooding.
Remove any turf. Dig up plants and place them in a cool, shady area. Cover them with wet burlap if the weather is hot.
Smooth out the slope area with a shovel. Remove dirt from the higher end. Place it in the wheel barrow. Deposit the soil on the lower ends of the slope.
Check that the slope goes away from the house or any buildings.
Replant any turf or plants.
Spread purchased topsoil, sand or garden soil over the low areas. This works if you have just a small slope, or a very gentle slope, and building up the slope won't cause water to run off toward the house or buildings.
Rake the soil until it is level with the rest of the yard. Water it well to settle the soil.
Fill in any gaps that result from the soil settling with additional soil.