Wash the clams one at a time under running water, scrubbing off any sand with your fingers, a scouring pad, or a brush. If a clam is slightly open and doesn’t close when tapped on a hard surface, discard it. Try to pry open any clam that feels very heavy. If it’s full of sand, discard it.
Put 2 cups of water in a heavy-duty 6- to 7-quart pot or Dutch oven, cover, and bring to a boil over high heat. Add the clams and cook, covered, for 5 minutes (if the liquid threatens to boil over, set the lid ajar and reduce the heat slightly). Remove the lid, stir, and as the clams pop open completely, transfer them with tongs to a large bowl. (Recover the pot if necessary until the clams start opening regularly.) Discard any clams that have not opened after 20 minutes. If a shell is a little cracked but still pops open, the clam is fine to use.
When cool enough to handle, remove each clam from its shell over the bowl, leaving the adductor muscles on either side of the clam attached to the shell. Squeeze each clam gently over the bowl to capture as much of the broth as possible and then transfer the meat to a small bowl and discard the shells.
Strain the broth from the bowl and the pot through a fine sieve lined with a double layer of paper towels set over a medium bowl or large measuring cup. Close and press the paper towels to release more broth.
Dilute the broth with water (3 to 5 cups) until it is pleasantly briny, not overly salty. The meat and broth can be refrigerated separately for up to 1 day before using. Extra broth can be frozen and saved for another use.