You can go about this two ways.

One is to hang it upside down in a warmish, dark place -- an attic is ideal, but an unwarmish closet will work.

The other is to put it in a vase or jar with just a little water, keeping it away from light to the extent you can and not replacing the water as it dries.

Professionals use the first method, but they likely have barns or other buildings all set up for it.

If this is a mophead hydrangea, sources say to wait until the inner, fertile flowers are spent and the outer petals feel "rubbery" before cutting. We don't grow mopheads, so I can't comment on this from experience.