Sure: put a finely chopped fried rye bread into a three-liter jar (about 5-6 centimeters over the bottom), add 4 spoons of sugar, fill the jar with water and mix it, then pour a packet (6-8 grams) of yeast over the top (don't mix!) Give it a couple of days to ferment. When the kvass will be ready, just filter it, pour into bottles, close with airtight covers and put them into a fridge. You may add mint, honey, horseradish, ginger etc, according to your tastes. Also you may add a few berries of raisins into each bottle to make your kvass more carbonated like a sparkling wine.
As you can see, the recipe is very simple and in contrast to cola and other canned drinks, it does not contain any toxic chemicals. While cola kills you, kvass just makes you more healthy, because it regulates the activity of the gastrointestinal tract, improves the metabolism, prevents the growth of harmful pathogenic microbes and has a beneficial effect on the cardiovascular system. Also it's very tasty, so it's a major drink in my county, which can't be ousted by cola, ice tea, sprite, fanta etc. Actually even the Coca-Cola company has its own brands of kvass. But... any commercial kvass is much worse than a home-made one, because the canned kvass does contain lots of unhealthy chemical additives like stabilizers, preservatives etc.
P.S. Usually we use a special syrup made from rye malt and rye flour, instead of fried bread, to save the time (you need just 3-4 spoons of it to make 3-liters of kvass). You can usually buy in any Russian grocery and it looks like this:
P.P.S. If you make kvass by a classic recipe, it may contain up to 1.2% of alcohol, so it's not recommended to drivers in Russia. That's not because it makes you drunk (kvass is recommend even to kids), but because even a single drop of alcohol in the blood of a car driver here makes him officially DUI.