There are tens of thousands of affiliate/publisher programs out there but understanding which type of program and which model best suits your site and your users is a difficult decision to make. Let's look at the different ways to make money on (or from) a website in order of the most-utilized/common.
CPA - Cost Per Acquisition
If you have ever signed up for an affiliate network you will likely be very familiar with cost per acquisition. CPA is by far the most common payout structure for merchants and in turn affiliate networks and affiliates. In CPA, affiliate websites direct their visitors (through display banner advertisements or sponsored text links) to the merchant's website. When a sale is made, the merchant gives the affiliate the pre-agreed commission.
CPL - Cost Per Lead
Those affiliates/publishers that are performing at an effective rate are those which may also have the luxury of promoting offers on a CPL basis. Cost per lead means that you, as the affiliate, direct website users/visitors to merchants' websites not in the hopes of them purchasing anything (although some programs have a CPA/CPL hybrid offering) but rather providing their information via filling out a form, signing up for a service, requesting information, etc.
CPC - Cost Per Click
Most publishers and affiliates starting out opt for cost-per-click offers. In CPC, affiliates receive a percentage of the advertiser's bid price. The most popular CPC affiliate/publisher program in the history of the 'Net is Google's Adsense program. The challenge for affiliates is in producing content that drives a sufficient amount of traffic so that even the small percentage of clicks which happen on these ads is profitable.
Cost Per Impression
CPM - While not as common as it once was, CPM (cost per thousand impressions) is now typically the reserve of websites with large amounts of traffic and sophisticated targeting and segmentation capabilities. CPM deals are often extended to publishers/affiliates by merchants when the site is established and afforded some authority by its users. For merchants, CPM deals are ideal for branding and awareness campaigns. For affiliates and publishers, CPM provides a low-impact way to generate profit from traffic without much leg-work.