So say you have $1MM of dirty money.
You go pick up a random painting, or scribble on some canvas yourself. Then get your art appraiser friend to say your painting is worth $1MM.
You then sell that painting at auction to another friend for $1MM. Cash only. Private transaction.
But the cash never actually changes hands. Your friend gets the painting, and you claim that the $1MM of dirty cash you had laying around was instead proceeds from the art sale.
Now there are tons of other examples out there with different methods. But it generally all comes down to selling an object that cannot be objectively valued for an all cash price.