Almost all standard coffee makers require a coffee filter. However, this doesn't mean that running out of store-bought paper filters should keep your from brewing coffee. Homemade filters, made of either cloth or paper towels, work well in a pinch. Cloth filters can even be reused, if necessary.
When filtering coffee using paper towels, it's best to use plain, white towels. Tear off two full-sized paper towels and double them over at the joint. Center the paper towels over the basket, then press down. Poke around the inside of the filter basket to make sure that the towels completely line it. Trim away any excess paper that sticks up above the rim of the basket. Fill the basket with grounds and slide it into place. Make sure that the basket fits easily into its compartment. This technique does not work well with other types of common paper products, such as napkins and toilet paper. That's because other items aren't designed to hold up as well to moisture.
Using a homemade cloth filter is a great way to cut down on waste. It's best to use a tightly woven, white cotton fabric, such as a clean handkerchief or square cut from a tea towel. Fold the cloth into quarters, then press it down into the filter basket. Either trim away or fold over any material that extends above the upper edges of the basket. Hand-wash the cloth filter between each use, but don't use any detergent or soap. Residue can creep into your next batch of coffee.
Filters made from a new pair of pantyhose are great for cone-shaped filter baskets that you pour hot water into. They are not ideal for electric coffee pots, as the heat can melt the nylon. Cut off the pantyhose at the ankle and insert the toe into the basket. Fully line the basket with the pantyhose, then fold the excess material over the sides of the filter basket. Fill the basket with coffee, then pour hot water over the grounds and let the coffee seep into a cup. Dispose of the pantyhose after use.