Begin by prewashing your drop cloth to remove sizing. Then cut to the desired size allowing for a simple hem all the way around. My drop cloth was already the perfect length, so I only had to hem the two long sides. I then folded the length in half (see the crease) and placed painter's tape about 1/2 inch from the crease on each side. No need to measure exactly. Remember that you are going for a vintage look. It doesn't need to be perfect. Then open the cloth and you will have a 1 inch wide center. Add another row of tape on either side, again at 1/2 inch. Your tape should look like this.
I used FolkArt brand acrylic paint to which I added some FolkArt textile medium - 2 parts paint, 1 part textile medium. This will keep the paint soft and flexible once it dries on the fabric. I simply applied the paint with a foam brush. Not too heavy and neatness really doesn't count here. If you want your fabric to be washable, FolkArt recommends setting the paint with a steam iron. You can find the details here.
And here is the result.