Today I was showing Boy some "flowers" that I have to add tie-downs to a tarp or any plastic sheeting. These are little plastic pieces that are called tie-down buttons. They are reusable and easy to install on any tarp. They are only about 50 cents each but you don't even need to buy any if you don't want to. You can make due with quarter to half dollar sized round stones or even large buttons.
Why do you want to have some of these or at least know how to make them? They are designed so you don't need to use the brass grommets. That way if you need to secure a tarp you aren't relying on the placement of the grommets if they aren't in the right place or if they are ripped out. I've seen people punch holes in their tarps because they don't have grommets or the grommet is ripped. Then they have to get duct tape to tape up the hole so it doesn't ruin the rest of the tarp. Tie-down buttons are easier. You can also use any plastic or piece of material; you don't have to specifically use tarps (perhaps securing a tablecloth to the picnic table).
How do the tie-down buttons work? You put the little button underneath the tarp. You put the top piece on top of the tarp and slide it over the tarp and button. Pull on it until it is tight. Then you can tie your rope into it. If you don't have these buttons you can improvise to make your own using a round pebble or actual button. If you use a rock you'd put the rock under the tarp then take string and on top of the tarp knot it around the rock. Here's some examples that I found in Flood Fighting Methods by the state of California.
I had a leak in my trailer roof (the vent cap blew off) and the easiest way to tarp the trailer was to put plastic over the trailer and every few feet put in a button tie, then tie the rope to a rock. It kept the plastic on even during heavy windstorms. Try it using a plastic bag as your tarp. Take a marble and put it underneath, then tie some string on top. You'll see how easy it is to improvise and not make you reliant on grommets.