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Consider machine washing them. Fill your sink with warm, soapy water. Drop the slippers in and agitate them. Let them sit. Rinse the slippers. Remove the excess water. Let them dry.
Cotton is one of the most common slipper materials. Just like cotton clothing, all cotton slippers will be washing machine safe.  Use warm (not hot) to make sure you don’t shrink the slippers. Use a gentle cycle that won’t bang them out of shape. If you want to toss them in with the regular wash, use a washing machine bag like you’d use for a sweater.  Use a low heat setting to dry. You can also allow them to air dry. If you don’t want to risk machine washing those slippers, then you can hand wash cotton slippers. Use a stopper and fill your sink with warm, soapy water. A small dose of a mild laundry detergent will do. Hand-washing detergents will instruct you how much to use. You want to make sure that the soapy water saturates the material. Use your fingers or a gentle cloth to scrub the inside lining to penetrate the grime. The soap solution won’t hurt the cotton. Give the slippers a good ten minutes to soak after you give them the mild scrub. You’ll see the soapy water changing colors as it leaches out all the funk. After the slippers have soaked, go ahead and let the water out of the sink. Turn the faucet on at about the same warm setting as before and give the slippers a thorough rinse. Squish the slippers as you rinse like you would to get excess soap out of a sponge or luffa. You can refill the sink with clean water to rinse them. Let them soak for ten minutes. You can also rinse them under the running faucet for two or three minutes to get all the soap out. Don’t actually wring the slippers. This can misshape them. Instead, press down on them at several points to remove the excess water. You can also squeeze them in a towel to absorb the excess water. Set the slippers aside to air dry. You can also use a warm setting on a blowdryer to dry them out. A blowdryer will also fluff the soft, cottony insides of the slippers.