You need to be absolutely sure you’re willing to take on the responsibility, as once you start taking paying customers, you’re entering into legal arguments that could come back to haunt you if you ever back out of them.
You also need to be confident you can handle all the financial questions that will arise – such as “Do I need to pay taxes during my first year as a self-employed individual”, “What is the difference between running as a company and simply reselling space” and “What will happen if I get sued”
If, after thinking about all these matters, you are willing to take responsibility for what may be someone else’s life’s work, responsibility for avoiding hackers who’ll try their very best to hijack your system and use it for nefarious ends (make no mistake, you WILL be held responsible), then you can pay a visit to one of the hosting resellers.
To start small, you can simply sign up for a shared reseller hosting account – http://www.fuitadnet.com/ has a number of examples, although you would be strongly advised to research the level of customer satisfaction with whichever company you look at.
If you want to get more serious, you can lease whole servers through companies like http://www.ev1servers.net/, where they turn it on and give you an internet connection – the server may or may not come with pre-installed webhosting packages that make it easy for you to just hand out the keys to your customers.
Companies like EV1 scale up with you, to the point where you may be leasing dozens of servers from them and have your own dedicated rack space within their datacenter – typically, while you’ll be limited on bandwidth to the internet, traffic between any machine you lease is not counted.
You can decide to buy your own equipment instead of leasing it – at that point, you’ll probably be looking at “colocating” your equipment with a larger ISP who can provide backup power and multiple internet connections (in case one goes down), but you’ll probably want to hunt for a company/location closer to home, as you’ll probably be responsible for the hardware yourself and if a reboot is needed, may have to make a personal visit to the servers.
Finally, you can go the whole hog and have your own location and highspeed connection, at which point you answer to noone but your data carrier. To run a serious hosting company at this level becomes extremely expensive, however, as to do things right you need to worry about duplicates of everything, power, connection, fire suppression, etc. You /could/ just hook up a single server to a “lower” speed high-speed business class connection (the Terms of Service of home-class connections usually prohibit hosting servers) but then you’re back to all the moral questions that opened this answer.