Obligatory Joke: As Much as it Wants!
But seriously... the other day, my daughter and I were talking about dragons. She'd been re-reading Wizard of the Coast's "Practical Guide to Dragons" series, and, well... let's just say that while the art is great and the writing is good, the books could be used as poster children for the "Writers Cannot Do Math" trope.
They thankfully don't even try to give amounts that dragons eat. So, when she asked about how much that might be, my physics/computer science background came out, and I started doing some estimating. I started with the knowledge that a working cart horse needs 30 to 45 pounds of food a day. Estimating the horse's weight at 1000 to 1500 pounds, and looking up the Calories / pound of various foods, I estimated that an animal of the same weight eating meat would need about 1/6 as much food... for 5 pounds of food per day per 1000 pounds of body weight, of 10 pounds/day/ton.
We then decided that since dragons fly and breathe fire, they'd likely need more energy. So we decided to somewhat arbitrarily double the amount, to 20 pounds/day/ton. Given a 7-ton dragon (the weight of a large tyrannosaur or elephant), that comes to 140 pounds/day, or 980/week... that is, about a sheep a day, or a cow a week.
Of course, that's presuming the animals being eaten are 100% meat, which isn't too likely. So let's make it two sheep a day, or two cows a week. (Some of which will likely be wastage.)
However, predators tend to eat less regularly, eating all they can at a meal, then not eating for a considerable length of time. While some types of reptiles can eat their own body weight or more, most animals cannot. If we assume a dragon can consume up to 1/4 its own weight and still fly, which seems reasonable (and about matches how much a lion will consume at a meal in the wild), then our 7 ton dragon will eat about 1.75 tons at a sitting, or 3500 pounds - which is about 3.5 cattle.
That gives us a dragon who kills and (mostly) eats four cattle about every two weeks. This doesn't seem unreasonable, and would certainly make a big impact on local farmers, especially when you consider that each time the dragon feeds, it's likely to panic the herd of cattle it's feeding from, causing additional injuries (and possibly deaths), knocking down fences, and so forth.
Later on, I looked up how much predatory birds eat, thinking that would be a reasonable model for flying dragons. The relevant formula there is:
Maintenance Metabolic Rate (kcal/day) = 1.5 (78 (weight in kg 0.75))
(found at The Modern Apprentice, a falconry site)
This is adjusted for bird activity, with multipliers from 0.7 for an inactive bird, to 1.3 for a highly active bird. To two significant digits, we get 83,000 kcal / day. Now, here, we need to note that food industry Calories are actually kilocalories. Using beef's roughly 850 kcal / pound, we find that this is 98 pounds of beef / day, a bit less than the 140 pounds / day we arrived at above. However, digging into some other sources, carnivore digestion is only about 90% efficient... and, of course, we have the fact that a cow isn't pure beef. Between those, we can probably keep the above figure of 20 pounds/day/ton, and not be too far off.
(I also remembered later that Gregory Paul's Predatory Dinosaurs of the World, which I am a happy owner of a copy of, has an appendix on predatory dinosaur energetics. There, I found a similar formula, of 140 (weight in kg 0.75)).
The one thing we might want to do is use the weight 0.75 scaling factor from above, when figuring larger weights, at least. So, for a huge dragon, say weighing the estimated 90 tons of the largest titanosaurs, multiply by ( 90 / 7) 0.75 = 6.8... for a creature that eats around 25 cattle every two weeks!
Of course, if dragons hibernate, then this changes significantly. Bears depress their metabolic rate to about 25% of normal when hibernating - using that model, our huge dragon might each 25 cattle, then return two months later.
Another alternative would be to use cold-blooded animals' metabolic rates, which are about 1/10 that of warm-blooded animals... so our dragons would eat about once every 5 months. If they also hibernate, that could be every couple of years!