Adult female moths lay larvae in carpets, which, when hatched, will munch away at a material called keratin. Keratin is found in natural fibers such as wool or silk, making any carpet or clothing with any such content a target. It’s also present in organic matter such as dead skin and hair (that includes pet hair, so if you have a cat or dog in your house you might need to pay special attention).
The adult moths themselves don’t eat the carpet and only live a few months, but one female can lay up to 200 eggs at a time, so it’s not difficult for an infestation to get started.

That depends. A larva can develop into a moth in as little as two months if it has the right conditions of heat and humidity.

During colder parts of the year maturation is slower (though central heating can create a year-round problem). At the other extreme, a larvae can take a couple of years to develop.

The key is to act quickly once you see any signs of moth activity. Given the potentially fast lifecycle of a moth and the number of eggs that an adult female can lay, you can quickly be facing a household problem as the moths spread, attacking carpets, rugs and other fabrics made of wool, cashmere, silk, leather or fur.

If you have carpet moths, a professional deep cleaning is highly recommended. For other types, you want to directly tackle the infestation. Remove any contaminated food (so-called pantry moths like to lay their eggs in dry goods); if they are in your clothes get them in the washing machine in the highest heat possible and then tumble dry (check the care label first) Then get the vacuum out and go over everything in the vicinity, from the floorboards to the walls (don’t forget to immediately chuck the vacuum bag in case it has larvae in it).

The best way is to make the environment unappealing for moths. That means sealing unseasonal clothes in airtight bags (make sure you wash them beforehand), while foods go into airtight containers. Then vacuum on a regular basis, as moths can be drawn to crumbs and dust.

Make sure to get behind furniture and into any corners or crevices. To be thorough, periodically remove sofa cushions and take off any removable cover to give them a shake or wash.

It’s also a good idea to give any rugs, furniture fabrics, cushion covers and clothing an airing as moths like humid spots. If possible, hang outside in sunlight (especially if anything has been in storage awhile). Finally, place homemade moth repellents in high-risk areas; cedar wood Vinegar, mint or moth balls will also keep the pests at bay.