Short films are like food. They can be prepared with expensive ingredients and still end up as a disaster. They can also be prepared with left overs and turn out unexpectedly well. So, the outcome is in the hands of the cook and not the ingredients.
Having said this, it is safe to come to a conclusion that the budget of a short film doesn’t affect its success in a major way. So, it is better to cut short expenditure wherever possible.
First things first, the script has to be a viable and strong one.
The locations must be accessible and must not involve spending money just to access the place. Some places require permission to gain access. Therefore, in such cases talk diplomatically and politely to get permission. Pull out all tricks from the book. Explain how it is a film with no budget because this might come in handy.
Call in your friends, relatives or even your neighbours to be a part of the crew because this cuts out the need to find and pay for a crew. Use the technically sound ones for the technical work. Use the ones that are not skilled enough for field work because it requires a lot of man power. But, make sure of paying them in kind. That is, provide them with food because that will keep them going.
If the cost of the equipment bothers you, rent them. There are a lot of places that rent filmmaking equipment at low prices. It is also not wrong to borrow it from someone. Instead of buying a DSLR for shooting, it is much easier to rope in your friend who owns one.
The final problem would be casting the right people for the part. So, it isn’t a walk in the park. Try and work with professionals that don’t charge you beyond what you can offer.