I've sold a number of SaaS businesses and acquired a software business in October.
There are several main avenues:
1. Self-fund - Either take money out of your own pocket, or sell assets you own
2. Take a loan - Friends, family or banks. Expect lower amounts from friends and family (depending on what circles you travel in), but more favorable repayment terms. Flip that around for banks.
3. Take on a funding partner - Give someone a piece of equity in return for them investing their funds into the biz
4. Bootstrap with profits from another business - Use cashflow generated by another business to finance your next acquisition
5. Earn-out option - I've heard of some folks setting up a deal with the owner of the business where they pay a partial sum to acquire the business, then pay a portion (or all) of the subsequent monthly profit after ownership changes hands, for either a defined amount of time, or up to a certain amount to the previous owner, in order to "earn out" the rest of the balance due.
6. Find a suitcase full of cash down by the river ;)
7. Work-to-own - Going out on a limb here, but if you were in possession of a skillset that was valuable to the business, you could conceivably offer to work for equity, instead of getting paid for your time. Strictly a theoretical scenario, but I'm just thinking outside the box here.
I hope that helps! Feel free to gimme a call if you have more questions about this. ~Jason