Sandblasting gives the best effect, but if you don't have the equipment or want to spend money acquiring it, and can't/don't want to just apply the stencil/masking and take it to someone else to sand blast, acetone is the way to go.
I'm skipping the other mechanical methods, as they take a lot more time, patience and skill to give pleasing results (e.g. trying to use a rotary engraving tool for the first time usually leads to cursing and disappointment).
Don't use too much acetone at a time, and don't pour or drip it onto the surface as any drips will also react immediately anywhere it touches the surface.
Work in a well ventilated area, as acetone is very volatile, and breathing the fumes is not a great idea.
To be safe, you can dab acetone on using a cloth, cotton wool or even ear buds for smaller areas.
Make sure your masking/stencil seals properly to the surface and doesn't allow liquid to get underneath the masking and rinse with lots of water immediately after application.
The reaction is much faster than when you etch glass. You can always apply more acetone if the initial effect is not as pronounced as you want.
If your piece is not too large, you can also create the frosted effect by coating your entire piece in parrafin wax (inside too) then removing the wax over the areas you want to frost/etch and exposing the piece to acetone fumes in a closed container over a period of time. This requires some experimentation to find the correct amount of acetone for your container volume and the amount of time to leave your acrylic in the container, as different types of acrylic surfaces will etch differently.
If you are too impatient to vapour etch, you can use a fine atomiser spray.
This method is actually less likely to end in disaster than most types of stencil or masking, as all the remaining surfaces, inside and out, are protected by the wax.
When finished, the wax can be removed using very hot water.
If you make a mistake or the finished surface is too rough, use old fashioned white toothpaste to buff (ideally you would use a 3micron diamond polishing paste, but why break the bank for simple craft projects).
Some acids can be used to etch some plastics, but this is not a good area for experimentation unless you are very sure of your raw materials and the chemical reactions you can expect. Using the wrong combination can leave you with a permanently sticky surface or a melted puddle of plastic.
Lastly, there are several types of "frosting spray" or "sandblast spray" paint available at most building/home DIY stores that are made to mimic the frosted glass look. They are not that wonderful, but it is an option. Just make sure you use the type made for plexiglass, not glass.