Removing paint from treated lumber works much the same as removing it from regular wood. There are three primary methods that are used--sanding, chemical stripping or applying heat and scraping the paint off--and each works easily and equally as well.
To properly sand the paint off, start with a low grit sandpaper (75 or lower). The grit number on sandpaper relates to how many grains of sand are in a square inch of the sandpaper. So, the lower the number, the less sand grains on the paper. Work the sandpaper against the surface in a circular and varying manner. You can also use an electric sander, generally a random orbital sander is preferred so it evenly sands the surface.
Chemical stripping is another method. Apply the chemical stripping agent with a rag or sponge. Make sure to wear rubber gloves to protect your hands. Wait the recommended length of time (waiting times vary), and then wipe the stripping agent off. The wood will be good to go after allowing it to fully dry.
A heat gun can be used to loosen the paint allowing it to be easily scraped off with a metal scraper. Simply point the heat gun (available at most hardware and paint stores) at the painted wood, and scrape the paint off.