There are only two ways to finance a start-up operation: with debt or with equity, or some combination of the two. With debt means you go to the bank or a lender like the SBA and apply for a loan. You’re going to need to be able to convince your lender that you know why the previous owner could not make the business work and that you know how to make it work. So, give some thought as to how you will address that.
Financing with equity means that you find an investor who would be willing to put up some capital for an ownership interest in the business. This could be a friend, relative or associate, or venture capital business.
Applying for grants and government loans is a good idea if you have time. The wheels move very slowly in most cases. It may be better to find short-term, start-up financing at the local bank or venture capital company (or both), then apply for the government grants and loans that will take out the short-term financing and set up a long term repayment (debt) / buy-out (equity).