Without a Website
Yes, if you do not have a website, it can be done. You can still make money online. There are two primary ways. One way is to join affiliate marketing or pyramid schemes. You recruit people under you and those people recruit more people. Then you will all have to promote products and you will earn. Some programs pay you to just surf the Internet and if you have people under you, and they surf the Internet too, you will also make money.
Another way is to work online. There are jobs on the Internet where you can work at home. You need to be a typist and type reports or do data entry and you will get paid.
With a website
If you have a website, you need to make sure that your website is legal and contains no offensive material. And then you need to get visitors to your site. Once you have enough visitors, you can try to get advertisors to advertise on your site and then make money. You can directly approach companies who need advertisement or you can join contextual advertising programs like Google Adsense, Kontera, Chitika, Bidvertisor and etc.
Making Money From the Internet all sounds simple but actually not quite. You need dedication and commitment to do that. But when you succeed, your success would be sweet.