Veganism has a reputation for being an expensive dietary choice, which is quite frankly unfounded. It can be expensive, if you buy lots of processed convenience foods - but those foods are expensive whether or not they are vegan. Buying whole foods like grains, dried beans, and locally-grown, in-season veggies is a good way to keep costs to a minimum. Shopping at markets is often cheaper than the shops, and when you do spend money, it goes to local individuals, rather than transnational corporations. Local shops like the Asian Grocery Store are often cheaper on certain ingredients like dried beans, and again, you're supporting local people, rather than Wesfarmers or Woolworth's. Stocking up on items when they are on sale or reduced-to-clear is another good strategy - even when something "expires" the next day, you can extend its life by freezing it. Or, forage! Look around your town for food plants growing in shared spaces, and help yourself!
Meal Planning. We don't do this. I know that it works really well for some people as a way to save money, reduce food waste, and stay organised. But it doesn't work for us. Instead, we shop at regular intervals - every Sunday, we pile our fridge full of produce from the markets. Then, we have a week to use it up. We just make a point to choose meals each day that use the veggies we have before they go off. Sometimes it means our carrots get a bit limp, or our eggplants go a little wrinkly, but when they get to that stage we just use them. No food waste, but plenty of flexibility. It works for us, but I'm not necessarily offering it as advice to anyone else.
Some slightly more time consuming ways to up your food budget savings. Most of these involve an initial expense, but in our experience these initial costs are really worthwhile.
Get a pressure cooker. The initial cost is worth the savings you will make in the cost of beans - dried are cheaper than tinned. The energy costs of cooking the beans are minimised by the pressure cooker, because it only takes 15-20 minutes on the stove. And it's not that inconvenient - an hour of bean soaking, then 20 minutes of cooking, and we like to freeze beans in empty jars for use throughout the week. And since canned food has "high levels" of the chemical BPA, it's a good choice for your health. And if you think about it, dried beans are probably a better environmental choice because they are lighter and smaller, so won't take as much fuel to transport. All around good choices! You can also use the pressure cooker to save time when cooking stews, dhals, and seitan roasts, for a quick midweek meal.
Get a bread maker. Another initial cost which is totally worth it. We get fresh, multigrain bread for about $1 a loaf, including electricity. And we use it to make other bread-like products, like pizza dough and hot cross buns. And, we can use our bread maker as a jam maker. We store our fresh, sliced bread in the freezer, so whenever we want a piece it's as soft and delicious as possible after a few minutes at room temperature.
Grow things. We used to live in a flat with a small courtyard with inadequate space and lighting. But we found a few robust plants that we keep on hand. The best thing to grow, even if you only have a window-sill, is herbs, because they are expensive and not that fresh from the shops. We currently have oregano, thyme, garlic chives, basil, and mint. We also grow a vigorous tropical variety of spinach. Think about your climate, the foods that are fairly expensive to purchase, and the space you have, and do a bit of research to find out what you should plant. Now that we have a house with a big yard, we have planted so many things - a few are ornamental native plants, but the vast majority are edible. Check out our list here.
Make your own soy milk. This is a bit of an advanced level money-saver. Again, it is a bit of an initial cost, but the savings here are probably the most substantial. The process can be time consuming, and is if you follow my initial advice. But we've changed our strategy since then (which I should really post about). We made a batch every 4 or so days, and get a litre of organic soy milk for around 20cents. In addition to the milk, you get okara, which can be used as a substitute for mashed/blended tofu in certain recipes, adds a protein- and fibre-boost to granola, and is like a free bonus.
Other appliances can be useful, too. A food dehydrator will let you store fruits and veggies for later use, which is especially helpful when you grow things, forage them, or have friends and you have a glut of one thing. Fruit roll-ups and dried fruit make great snacks, and veggies can be dehydrated for later use in soups or stocks. A dehydrator is also a good tool for making granola. An ice cream maker is an entirely superfluous appliance, but the ice cream is excellent - much cheaper, but also creamier and tastier than any I can buy in the shops.