I can usually tell rayon just by feel--it feels 'slippery", and cotton doesn't. Often I can tell if there is polyester mixed with the cotton by ironing the fabric after I've washed it. If you iron on the hottest setting, which is cotton, the fabric with polyester in it gives off an unpleasant, pungent smell, while 100% cotton just smells sweet if there is any odor at all. I know you can also examine the fabrics under a blacklight and some synthetics show up somehow. I'm unsure what they look like--I'm guessing they glow. I've never done it, so I can't say for sure.