As clean as cats are, every once in awhile they need help from you in making sure their fur stays smooth and tangle-free. Tangles can happen for any reason including the cat's inability to reach certain parts of its body or you might have a longhair cat, which are naturally prone to tangles and dreadlocks.
Take the comb and run it through your cat's fur. Take note of any places where the fur just doesn't seem to want to come undone.
Tug with the comb at the areas where you think there could be knots gently to make sure they don't just need more force.
Feel the fur with your fingers to determine how long the clump is.
Firmly comb at the clump while holding your cat's skin down. You want to be pulling at the fur, not pulling the skin with it.
Hold the cat firmly, nestling them close to your body, if combing doesn't work. This will keep your cat from bolting as soon as you're distracted. Try holding them around the chest or neck area with your entire arm, leaning down to fold yourself around them. It may seem a bit much, but there's nothing more frustrating that having to chase your dishevelled pet down before they bolt under a bed.
Coo gently to your cat. Tone is a big thing here; don't get excited or nervous, as your cat will pick up on that, and become even more agitated.
Pull the clump so it stands straight out from your cat's body, and hold it as close to the skin as you can.
Using your finger as a guide, slowly move the scissors so the clump is between the blades.
Double check that no skin will be cut, and slowly slice through the clump.
Try to have more than one person when holding your cat for anything; not only will the extra person help calm them, now there's another set of hands to grab them if they managed to scurry away. If your cat runs and hides, don't chase them. Clumped hair is unsightly, and itches, but it's not a life-or-death situation. Let your cat calm down, and reapproach when they look relaxed.