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If you are leveling a small area and it is mostly level, you probably will not need to remove the grass. However, if you have a large area and a lot of leveling to do, removing the grass will be much easier. A simple shovel is all that's necessary for a reasonable amount of space. Depending on how much ground you have to cover and what will be going on the ground afterwards, you'll need to level your land with differing mixtures of soil, sand, and compost/manure fertilizer. If you want to grow grass in this area, the cover will need to be nutrient rich. If you want to level for a pool or shed, soil and sand will do just fine. Use a garden rake to spread the material evenly, checking using your level and a measuring tape to make sure it's staying level. If you have a large area to cover, there are small versions of ground moving equipment that you can rent from your local hardware store. They will be able to advise you on what will work best for your property. If you are leveling a small area, you can tamp the soil using your foot and the bottom of your rake. If you are leveling a large area, or it is especially important to keep the ground level (such as if you are building a structure), get a tamper or plate compactor to compact the soil. Give the soil plenty of time to settle. It needs at least 48 hours, if not several days or weeks to settle properly. Mist the area with water if your area does not get rainfall during that time.
Remove the grass if necessary. Add your ground cover. Spread the topsoil. Tamp the soil. Let it settle.