Walk the area where you plan to start your rock garden. Make sure you remove any sticks, rocks or debris from the area before you begin tilling up the grass, weeds and roots.
Rent a garden tiller from your local equipment rental store. Depending on the size of the area you plan to till, you should be able to complete tilling within the typical 24-hour rental turnaround time, so you will only have to pay for one day's rental.
Till up the grass, weeds and roots in your rock garden site, while wearing long pants and closed-toe shoes to prevent harm from flying debris.
Remove the loosened grass, weeds and roots with a shovel, and place them in a wheelbarrow for later disposal.
Saturate your freshly tilled area with white vinegar. Make sure you have enough vinegar to pour over the entire area. This will kill any grass and/or roots that may not have been removed by the tiller.
Place your black plastic sheeting over the ground and secure it on the ends with rocks to weigh it down and keep the sheeting from blowing away. Keep the black plastic sheeting over this area for at least two weeks to prevent grass and weeds from growing.
Remove the black plastic sheeting and begin designing your rock garden.