lots and lots of hoovering.
Put all clothes and bedding through a tumble drier, as the heat will kill eggs, then immediately put into crates or sealed plastic bags (with the chemical) to prevent any new eggs being laid on the clean fabric. The mothkillers are usually only enough to treat half a cubic metre, so in a large wardrobe you will need several, and to keep the doors shut. They usually last 6 months before needing replacement.
Put all clothes and bedding in those plastic crates with lids, or in the large, transparent plastic bags used for recycling, and tape shut. You can put a mothproofer in each crate (it should be one that contains Transfluthrin, it kills adult moths, grubs and eggs. The vapour has to be concentrated in a container, or a closed wardrobe, or a door. The chemical is quickly broken down by sunlight, so it will be strong enough inside the closed container to kill moths, but will dissipate and break down if released into the room. The mothkillers only emit enough vapor to treat a small space.
Lavender and Cedar smell nice but they don't kill or remove moths.
Hoover a lot, especially edges of carpets by the skirting board where they like to live, and behind and under furniture, and the corners and joints inside wardrobes and doors. I would usually recommend that after hoovering and wiping inside, you spray a Crawling Insect Killer on the hard surfaces. It dries to a lacquer that the insects takes in through their feet, it does not evaporate into the air or spread around like a powder.
Moths are attracted to the smell of clothes that have been worn by a woman, so wash or crate everything after wear, don't just put it away. Single men usually don't get moths (this is true!)