To get things going, here is the first properly profitable thing I did online.
eBay. It's pretty much where I started, and where a lot of other people start, the only problem is that it's not free. However you can start out with very, very little investment.
When I first started I was 15 and using my grandmas debit card (with her permission, of course). I saved up about £80 and bought some designer label sunglasses from an eBay power seller who promised they were genuine. I was young and naive so of course I believed him. I managed to sell about 4 pairs before I got warned from eBay to stop selling fake items or I would get banned. In the end I sold the rest off to a relative to make back my money while he went down to the pub and sold them off for a profit.
After that I learned my lesson. The next lot of good I bought was a sample order of unbranded motorcycle gloves from Alibaba. They sold pretty well, making between £5 and £10 in profit for each pair of gloves. After creating my template I could get 3 of these posted in 20 minutes, and I could wrap them in another 20 minutes, and I could drop them off at the post office while walking the dog in another 20 minutes. £15-£30 isn't huge money, but to a 15 year old it was massive. And all it took was an hour of work each day (plus about two months of saving lunch money and researching before that).
I think eBay is an amazing place to start. Tonnes of traffic and all you need is to spend time creating an inviting title and description. A few good pictures, set the price stupidly low and wait for the bids to come in.
The only down side is you need a bit of money to invest. However, there are ways to do these even if you are almost penniless. Find something in your house right now that you don't use but could be valuable. Sell it. Then use that money and walk down to the closest charity shop. Find something valuable looking and in good condition, buy it, then sell that. Rinse and repeat. Sure, chances are you might mess up a couple of times and buy something that won't sell. But keep trying until you make your first profit. I promise you, from that moment onwards you will be hooked!
So to all the people out there making money online. What would you suggest is the best way for a beginner to start?