At a minimum you'll need a web site - you can find good hosting as low as 7USD per month, plus 10USD for the first year's registration of your domain; tools to build a site are often provided by the host, and you can also download free tools like KompoZer. Clip art, photos, and the other stuff you need for a web site is also available free on the internet if you know where to go. As CurlyBen says, you're going to have to find a way to finance the business even if you do most everything else yourself. There are places that offer free web site hosting, but their packages tend to be junk and have hidden strings attached. Minimal investment to start an online business? I'd say 17 per year USD is the minimum for the website alone, but you're going to have to acquire technical smarts to do so without additional expenditures (or if you know someone who has such smarts, take him/her on as a partner). And you're likely to find things that cost additional money as you plan and implement your business.
You can sign up for affiliate programs, and make money that way. But you still need something to sell, whether a product or service; just providing affiliate links isn't enough. I've seen some people make a go of it on eBay selling a product for someone else. You could become an eBay expert and offer to open & run a shop on eBay for a local business. Again, there's a charge for opening an eBay store. If you know people who produce one-of-a-kind crafts, Etsy is a sort of online bazaar for craftspeople; you could open a shop for someone - perhaps even opening a craft co-op for people in your area on eBay and Etsy. But there you're going to have to invest at least a small amount in an advertising campaign to local craftspeople. So the amount of money you'd need depends on your business plan, even if you're starting a business on a shoestring.
Also, be aware that there are plenty of scams and multilevel marketing schemes out there that will offer the sun, moon and stars to you for a "small investment". Beware. There's no substitute for hard work and creativity. You may be a poor guy but you were resourceful enough to get access to a computer and an internet connection! Use that resourcefulness to your advantage as you plan a business.