How you protect nearby sidewalks, landscapes, or lawn art may depend on how you cover the surface.
If you choose to use a sprayer, you can simply lay the tarp on the ground or throw it in the bush. However, unless you have a partner who is willing to hold onto a sheet of plywood while spraying, you will likely be sending the paint where you don't want it.
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Then when you want to spray paint, check the corners to make sure the paint has reached all the points. If not, you can leave the door open due to weather or insect damage.
For those who choose to use a brush or roller, you can cover the landscape as you walk. When working on a section, you can only place a tarp, plank or other lining in the area where you are working.
When painting a fence, some people find it easiest to paint one side and one edge of each post or picket along its length and then go back to the beginning to paint the other side and edges.
When painting or dyeing outdoors, be aware of the weather. For best results, the new surface should dry for at least two days. So check the rain forecast. Also, depending on the time of year, you should know about morning dew and how long it stays on the surface.