Google AdSense is the most popular option under this category, but there are also others. Basically you need to sign up with the network and paste some code snippets on your website. The network will then serve contextual ads (either text or images) relevant to your website, and you will earn a certain amount of money for every click.
The profitability of PPC advertising depends on the general traffic levels of the website and, most importantly, on the click-through rate (CTR) and cost per click (CPC). The CTR depends on the design of the website. Ads placed abode the fold or blended with content, for instance, tend to get higher CTRs. The CPC, on the other hand, depends on the nice of the website. Mortgages, financial products and college education are examples of profitable niches (clicks worth a couple of dollars are not rare), while tech-related topics tend to receive a smaller CPC (sometimes as low as a couple of cents per click).
The source of the traffic can also affect the overall CTR rate. Organic traffic (the one that comes from search engines) tends to perform well because these visitors were already looking for something, and they tend to click on ads more often. Social media traffic, on the other hand, presents terribly low CTRs because these visitors are tech-savvy and they just ignore ads.
List of popular CPC advertising networks:
Yahoo! Publisher Network (YPN)