Plexiglas can be a rather tricky material to keep clean and polished. If not done correctly, you can scratch the surface and leave it with a cloudy finish.
Use Hot Water
The key to polishing Plexiglas is to use hot water. The water should not be boiling, but on the verge of it. This will help to remove the grime without scratching it.
The main ingredient is regular white vinegar. Add about a cup of vinegar per 1 gallon of hot water.
Clean Plexiglas First
Using regular cleaner and a paper towel, clean off the Plexiglas before you being polishing it. This will remove any of the large pieces of dirt, grease, and grime.
Soak Sponge and Polish
Soak a sponge in the container that has the hot water and the vinegar. Place the sponge on the top of the Plexiglas and start working from side to side. It is important not to rub the Plexiglas, but slide the sponge over the Plexiglas from side to side.
Wipe With Newspaper
Using a single piece of newspaper and fold up to about hand width. Using the same swiping motion, start at the top and wipe the water and vinegar mixture off the Plexiglas. Your Plexiglas should be clean and streak free now. If not, use a rubber squeegee to finish it off.