Why do you need money? You actually don't. What you need are the things you can trade it for. Vet care. Boarding. Gas. Dog food. Electricity. The list is endless.
The first step in increasing your cash flow is to look for free resources. Why pay for the entire Adobe Creative Suite when you just need to knock some flyers together? Do you really need Contant Contact for spiffy newsletters? How about Vertical Response or Mail Chimp as free alternatives, at least in the beginning?
The second step -- consider asking for what you need rather than for money to buy it. Many people would far rather buy you a bag of dog food than give you the money to buy that same bag. The payoff for the donor is far higher (see my post on Brown Dog Red Collar programs. )
Don't forget -- a donation of a bag of dog food is STILL a donation. It's called a donation in kind and you've got to keep track of those, too.
Once you've done those two things, move on to the nuts and bolts of raising money.