This is a good time of year to get small pickling cucumbers from farm stands and farmers' markets, but no worries if you can't; just slice up a big cuke or two and make pickles from that. They'll still be delicious.
Combine the water, salt, and vinegar in a small saucepan and bring it to a boil, then turn off the heat and leave the brine to cool completely.
Meanwhile prepare the cucumbers: wash them, trim off the blossom ends (that's the end opposite where it grows on the stem), and, if you're using large cucumbers, slice them a quarter inch thick, otherwise leave them whole.
Put the cucumbers in a large glass or nonreactive metal bowl with the garlic, dill and peppercorns layered throughout, then pour the cooled brine over all of it (if you're a bit short, simply mix up another batch or half batch and cool it quickly in the freezer before adding).
Lay a plate over the top of the cukes--one small enough to fit in the bowl, but large enough to cover most of the veggies, since it will help keep them submerged in the brine. Now leave the cucumbers for 2 or 3 days, until they are nice and sour to your liking. Transfer them with their brine to a large glass jar, in which they will keep in the fridge for a couple of weeks--though you're unlikely to have them for that long.