Start by cutting a square that is 48" on each side. You can make yours larger if you want a bigger tree skirt. This size is slightly more toward the smaller size in terms of tree skirts.
The average tree skirt is anywhere between 48 and 56 inches. So keep that in mind when cutting the initial dimensions for yours. Generally, the rule for tree skirts is bigger the tree, the bigger the tree skirt.
You may have to seam rip the edges if your drop cloth is hemmed around the edge. OR just cut the hem part off - up to you. Now, cut that square piece into as many patches you'd like in varying sizes.
It's helpful to keep the square shape in tact even as you are cutting the pieces up so you know how they're all fit back together when sewing. It might even be helpful to take a picture of the placement of all the patchwork pieces so you can reference it if things get mixed up later in the process of tree skirt making.
Next, start painting different patterns on each of the pieces. You can do simple patterns like polka dots and stripes, dashes, plus signs, etc.
If you need pattern inspiration, try pulling up mudcloth fabric patterns online. You'll find some really good ones to mimic that way.
Once dry, make sure the painted pieces are arranged in a square once again and take a photo to reference later if needed.