There are several ways to handle this. For example, your flowers can be left standing and simply removed the next spring!
This is our favorite method, as it also allows our native insects to nestle in the stalks and find precious shelter during winter. Furthermore, birds can find valuable and nutritious seeds to snack on in some of faded flowers, for example in sunflowers.
However, if the faded flower meadow in your garden looks a little too wild or chaotic, it can of course be mowed or cut in autumn.