Synthetic fleece or polar fleece fabric is actually quite stain resistant. Most liquids roll off fleece rather than soak in. If you find yourself with something stuck on your fleece fabric, try gently scraping it off with a fingernail or butter knife, if there is something stuck on such as fingernail polish or paint. If the stain is soaked into the fabric, don't wash it in the washer until you can ascertain what the stain is and treat it, otherwise you risk setting the stain for good.
Determine what type of stain it is, if possible. If you can figure out if it's a food, grease or ink stain, it will be easier to determine what type of product to use to get it out.
Soak the fabric in cold water to try and loosen the stain. Fleece resists water well, but if you work at the stain gently with your fingernail, you may be able to loosen it up.
Apply a commercial stain remover or detergent safe for the fleece directly to the stain with a sponge. Allow the detergent to set on the stain for an hour or so before rinsing in a cold water bath or putting in the washer.
Spray hairspray on an ink stain and blot it up as the ink liquefies with a rag or paper towel. Spray a little of the hairspray on an inconspicuous part of the fleece before working on the stain to make sure it won't damage the fleece.
Dab rubbing alcohol on oil-based stains to help remove the grease from the stain. Avoid using white vinegar on synthetic fleece as it can damage the fibers.