Usually, to clean a decanter, warm water and a swirl is enough. Detergent can be hard to remove and can affect the aromas and flavours of the wine.
An overnight soak will be most effective to draw out any stains. Wash the outside with hot water to get rid of sticky finger marks and then rinse the inside with cold water, this will keep the glass from getting foggy, and allow to drain, ideally on a linen cloth.
A deep clean is okay now and again; we use a splash of white vinegar and some cleaning beads.
A final polish with a micro-fibre cloth and you’re ready to go again!