Ok, so I know a bit about this.
First, vacuum, and then vacuum again.
Vacuum all of your carpets (obviously) and also your curtains and soft furnishings.
Then steam clean the carpet if you can. If you can't do this, use a steam iron and hover the iron, blasting steam at the affected area. And shampoo it. By hand if needed.
Adult clothes moths do little damage, it is the larvae that you really really need to look out for (and eggs, which will obviously become larvae.)
You need to treat ALL your clothes and blankets, etc, those in wardrobes and those in storage. Clothes moths mostly go after wool and silk garments and furnishings. Even if they haven't attacked your clothes yet they will find the dark recesses of cupboards and a handy supply of wool food irresistible at some point and then will come back for a second or third round at your carpet.
Clothes and blankets should be washed at a very high temperature. For anything like wool which can't be washed high due to shrinkage, put the items into plastic bags and put in the freezer for three days defrost, then repeat, re-freezing.
If you need to do this in batches, do not place treated items anywhere near untreated ones until the whole load has been done. Whilst your clothes are being treated, clean your wardrobe, ever single nook and crevice. Vacuum, and vacuum again.
Mothballs give some deterrence, BUT only in closed areas like chests and storage boxes. Anything that is regularly opened (like a wardrobe) will not be helped by mothballs as it needs to be airtight to build up enough concentration in the area to be a deterrent.
People say that cedar chests/balls are a repellant, but really the protection is very minimal.
Handily, there's
an ace little book due out soon with a section on this very subject.