Summarize:

Using a shovel or hiring someone with a backhoe, remove the top layers of grass and dirt from the marked-off driveway area. You might want to use a tiller to loosen up the soil and make it easier to dig out. The amount of soil you remove depends on how many layers of soil you are planning. You should dig 4-6 inches of soil for every layer of rocks you plan to put down. This doesn't have to be perfect since it will be covered by rocks, but your driveway surface should be pretty levelany areas that are deeper than other areas may lead to water pooling and cause mud puddles that have to be filled in with more gravel later. Use a mechanical compactor, have someone drive over the area with a bulldozer, or drive over the area repeatedly with a heavy vehicle such as a large truck. If you want to prevent grass and weeds from growing through your driveway, you may want to lay a weed barrier underneath your rocks. Weed barrier is a woven landscaping cloth that allows water to pass through it but does not allow weeds to grow through it, and it is available at most landscaping and home improvement stores. Weed barrier usually comes on a roll. You should be able to lay the roll down at one end of your driveway and unroll it until you have reached the other end of your driveway. Most weed barrier rolls are 4 feet wide, so you may need to get several rolls. Be sure the amount of weed barrier you buy matches or exceeds the square footage (length times width) of your driveway. If you are using landscaping timber or bricks to edge your driveway, you may want to place them before the gravel is delivered so that they can hold the rocks in place. If you do not want a border, you can skip this step.
Dig out any grass and topsoil. Level the surface of the driveway. Compact the dirt. Lay down a weed barrier. Place your border.