The best methods that I have employed in order to reduce costs are:
1. Join a club. You will meet nice people with similar interests that have surplus fish and equipment. This is smartest thing any hobbyist can do.
2. Build your fish room around your tanks, or keep your tanks together in a small room. If your fish room is large and only has a few tanks, you will be loosing too much heat to the air. A small room full of tanks will take less time to warm up, and stay warmer without the need for you heat source to turn on.
3. Keep fishes that like the water you live with. You will find that your fish are healthier and you will waste less money trying to manipulate your water.
4. Get a reputable dealer for supplies that carries everything that you need. It does not matter who you buy from, just pick someone that you trust. You can always shop around for a bargain, but you need someone that you can rely on for the everyday essentials that keep your hobby going.
5. Do not overstock you tanks. If you put too many fish into your tanks you will run into compatibility problems leading to stress and fish losses. In overcrowded tanks disease is more of a concern. You will also spend more time changing water. Tanks that are less crowded require less attention. Remember, time is money.
6. Buy your food in bulk and keep it frozen.
7. Shop for fish food where you buy your food. Human grade food is the best food and your fish will agree. Sometimes you will find it to be cheaper too.
8. Find alternatives for aquarium decorations. If you are trying to save money, then do not even think about buying "aquarium decorations". I use mainly clay pots, pvc pipes, halved coconut shells, and flagstone slate. In the past I have also used fake plants that I bought at a craft store. The only aquarium grade decoration that I buy is wood because I am not confident that the wood I find will be non-toxic to my fishes. Many people do collect their own without any problems.
9. There are alternatives to aquarium gravel. I use pool filter sand for gravel. I should note that you have to be mindful of any rocks that you add to you aquarium. Many rocks will manipulate you water chemistry, so if you are uncertain of how a stone influence your aquarium please test it out first.
10. Reduce your lighting whenever it is possible. Lighting can be one of your highest operating costs, or something that you do not even consider into your budget. Not every aquarium needs a light directly above it. Many of my tanks are simply light by the room itself, or by the tank next to it. Your tanks really only need a lot of light if you are growing plants. Fish need light, but not much.
11. Reduce the number of power filters that you run. You can save some money if you invest in a large air pump and filter most of your tanks with air driven sponge filters or corner filters. You can even build your own sponge filters, I have never done this, but I hear it easy.
12. Reduce the materials that you need for filtration and find alternatives to aquarium grade products. I found that poly quilt badding works great for mechanical filtration and it goes into all of my wet/dry filters. I have cut out carbon completely, because it is too expensive. There are lots of great alternatives for bio media.
13. In general, try to rely on the least amount of supplies as possible. Fish really only need clean water and good food, everything else is just something that you need.
14. Whenever possible DIY.
These are just a few things that I have learned along the way and I hope that they are helpful to you.