Well speaking from experience of a limited budget. The best solution to that is people power. So I Hope you have lots of friends how know lots of people. If you can get people interested and involved in your project, they are more likely to try and help out. e.g. if you have some friend who knows someone who can get you a certain prop, or into a certain location ect.
What sort of equipment do you have? It doesnt need to be amazing, but if you can get most of it without having to pay out lots for rental/buying stuff. It leaves you with a bit extra for props and stuff.
Cant say I can give much advice on getting it sponsored. Depending on the subject matter see if there is a local arts council or something like that?
And your best bet for getting it screened is Film Festivals. Unless its a very small local cinema, it is normally close to impossible to get something in there.
As for spreading the word, the easiest is to just use whatever social networking your already use. But just keep posting info and photos from and of the different shoots you do. People like photos
Not sure if this will be useful to you. But for my final year project at college myself and a friend made a WW2 based short film. Guess it sounds cliched

But anyway we did it with whatever money we had, which wasnt much. But we knew the main actor, knew an acting teacher who told us about one of her young students who would be good for the role. We got in contact with the local war reenactment group for advice and all the equipment for free. and it continued like that, just getting more and more people on board and interested. We kept a blog - which may be a bit useful to you, who knows
http://warfilmproject.wordpress.com/
https://vimeo.com/35545896