they are devils to get rid of and nothing is guaranteed.
First you need to find the source of the infestation. It might be the carpet or clothes (wool is especially favoured by moths). Look for the lavae and depending on the type of moth there may be maggot cases (like rice grains) lying around. Probably best to throw out whatever the primary infestation is on (it will be full of holes in any case). They like the dark, so it's proabably at the back of a cupboard or under the bed or something (or indeed all of these places).
Wash absolutely everything that is made of fabric in the room at 60C min or freeze in bags for about 4 days or dry clean. This includes the curtains. Hoover the carpet repeatedly - you may need to replace it to be honest if they are in there. You can get sprays but they only give the maggots a mild headache (the really effective chemicals are now banned) and don't destroy the eggs so you have to repeat. Don't hoover after spraying until just before the next spraying.
The eggs are too small to see and are likely to be in the smallest possible cracks behind skirting etc. and can hatch and re-infest at any time.
If they are visible in one room they are almost certainly beginning to infest the rest of the house so you need to wash everything & hoover madly everywhere else too.
You can get sprays and moth traps and deterents, but they're not much good. Sprays work to a degree, traps only attract the males (and unless you get them all before they've impregnated one female the cycle isn't broken) and the deterents are more to deter the first moth or two rather than repel an established infestation.
Err this probably isn't what you wanted to hear, but good luck anyway.
They are a nightmare. I had them in my last flat - only thing that worked was ripping up all the carpets and having hard flooring.
I've now moved into a much bigger house and we have them AGAIN. I feel quite despair gnawing at my soul. Am currently taking the ostrich position but I know I'll have to tackle them soon.
You've had great advice from snorkie. I would reiterate that you need to check carpets as well as clothes (ground zero for our infestation was the carpet under our divan bed). Still, if you're only seeing them in your spare room then you may be lucky to have contained them.