I almost feel embarrassed to say this, but last year I was so poor that I had to learn to get by on about 50-70 pesos per week for food - that would probably be nearer 80-100 this year. I'm getting by better now (paying native rent prices makes a big difference), but I'm still scrimping and saving in an effort to travel next year. Anyway, I'm not saying this to be smug, but rather to pass on a few lessons I've learnt. I should stress that I'm pretty much vegetarian, so I imagine that brings the price down a little. Anyway...
Don't try to have the same diet you had back home. I miss mushrooms, I really do. But I'm not going to pay 12 pesos for a packet I could get for 50p back in London. Zapallito will suffice. Likewise, I hardly ever eat cheese anymore, because unless you're going to pay through the nose, it's by and large awful here.
Don't buy from Jumbo and the like. Even Coto should be avoided if necessary. Get to know your local chinos; find out which items are cheaper in each one. If you live in a posh neighbourhood, head to a cheaper one to buy your fruit and veg - from a green-grocer of course. I live in San Telmo / Barracas, but often nip into La Boca (it's okay in places at certain times) for fruit and veg. Even the butchers are cheaper there.
Don't buy in bulk. It's no cheaper (sometimes quite the opposite) and in the case of veggies, will go off before you can use it. Mercado Central is great if you're shopping for three or four of you, but not worth it for one or two people.
A small investment in some luxury items in Barrio Chino can lead to long term savings. Stir fries and curries are very cheap to make, beyond toasted sesame oil and garam masala, respectively.
Someone mentioned stocking up on food and drink before they leave the house. Wise words.
Invest in learning how to cook rather than investing in expensive brands. A good cook can make cheap ingredients taste expensive while a bad cook can make expensive ingredients taste cheap.
Okay, here are a handful of dishes that have kept me going over the past year. I'm not a sensational cook, but I've met worse. Most are fairy obvious but all are fairly cheap:
Soup - yeah, I know. But it's very cheap, lasts forever, and surprisingly filling. If you want to eat cheap you can't turn your nose up at it. Leeks (although expensive, spread over 5 or 6 helpings are justifiable), onion, garlic, carrot, sweet potato, vegetable stock, butter. Yum.
Falafel - chickpeas/Garbanzos are dirt cheap. Throw in a few spices, an onion, a clove of garlic, lemon rind and (shhh, you heard it here first) grated carrot and you're laughing. You can make about 10-15 falafel burgers for 10 pesos. That's not 10 pesos each.
Porridge - dollop or cheapest available jam / honey for flavour. Nice and warming on a chilly morning.
Omelette - nowt wrong with an omelette once in a while.
Roast vegetable, cheese and breadcrumb bake - this is relatively expensive, but I made it recently and fed about 6 or 7 people for around 40 pesos. It's nice cold, so it keeps. It's a ball ache to go into detail with the recipe, but if you're really interested then PM me. Otherwise, just make something up. I did.
Stir fry - Perennial student / bachelor's favourite, I know. But there's no shame in cooking it once in a while. You don't need stir in sauce: ginger, garlic, soy sauce and toasted sesame oil for flavour. Serve with rice (cheapest brand is fine), cooked in stock and pre-fried with a chopped clove of garlic. That's a meal for two people for about 8 pesos.
Vegetable Curry - lentils and chickpeas are very cheap here. Don't make a creamy curry with coconut milk - it'll treble in price. Go for the spicy kind instead. For other ingredients, you'll need to do some substituting for whatever's cheaper locally. Hola zapallito.
Quiche - one sheet of pastry, 3 or 4 eggs, dash of milk, packet of spinach, small onion, tomato, clove of garlic, bit of cheese. Probably less than 10 pesos. Feeds four. Nice cold. Has a french name, so it sounds like it should be expensive.
Veggie Burgers - lentils and/or chickpeas make the base. Then add whichever vegetables you like. Lentils can be bland, so you'll need to add plenty of other flavours (mustard and tomato puree comes into their own here).
Potato wedges or re-stuffed baked potatoes (mayo, cheese, ham, onion, garlic, oregano/thyme/chives) and salad.
On that last point: the staples of potato, rice, pasta, etc can seem pretty boring, but they are very cheap here. There are lots of ways you can cook them to make them more interesting. Actually, there are a few websites that specialise in finding you recipes based on the ingredients you have available - supercook.com is one of them. I s'pose you could just type in some ingredients that you know to be cheap here and see what happens.
Anyway, I've gone on enough here. Sorry if I've stated the obvious in a lot of cases, but perhaps it'll be useful to someone who finds themselves in the same situation as I did last year.