The most obvious way to tell if yarn is wool or acrylic is to read the label on the skein of yarn or article of clothing, according to Crochet Spot. Texture can also provide a clue, as can observing how the yarn reacts to fire.
Acrylic yarn is usually coarse, while wool yarn is typically fuzzy or hairy. However, some acrylic is made to imitate wool, so this is not always reliable. Holding the end of a long piece of yarn over a match can indicate whether it has acrylic in it. If the yarn continues to burn after you remove the flame, it is acrylic or a high-acrylic blend. If it immediately dies out, it is probably wool.