What do I need to do online billing?
You need a merchant account/credit card processor. No, you can't do it for free.
There is no safe and reliable way to process credit cards for free. Although, there are companies that will set you up for "free", but then charge you 10% per transaction. Don't pay more than 2.5%.
A popular one is authorize.net, feel free to check them out for their fee structure.