Green beans are fabulous on the grill. The trick, really, is keeping them on the grill. A smaller-than-normal spacing on your cooking grate will help. A grill basket works, too. Or, you can accept that you're going to lose a few to the fire and wing it.
Prepare a grill for high heat—you want to sear the beans quickly. Toss cleaned and trimmed green beans with a bit of olive oil to vegetable oil, just to coat them lightly. Put the oiled green beans on the cooking grate (placing them in a grill basket first, if you're lucky enough to have such an implement). If you're not using a grill basket, be sure to lay the green beans perpendicular to the bars of the cooking grate so they down all fall through into the fire. Cook until seared on that side and/or the ends, just a minute or two, use tongs to turn then carefully (this is where you'll definitely lose a few if you don't have a grill basket), and cook them on the other side for another minute or so.
Remove beans from the grill, put on a serving platter, sprinkle with salt to taste, and serve hot, warm, or even at room temperature. Delicious.