First, check the terms and conditions of the CPA offer you are going to promote. Each offer has its own limitations how it can be promoted. The most common ways of promoting a CPA offers are:
A double opt in list is generally required. Just emailing offers to a list of email addresses bought on ebay will probably get your CPA affiliate account terminated.
This includes standard PPC marketing, for example Google Adwords and Bing. Note that many CPA offers restrict what keywords you can bid on. Another thing to keep in mind is that direct linking to CPA offers on Google Adwords will get your account terminated.
Contextual in CPA marketing generally means PPV, Pay Per View, marketing. PPV is based on adware, users download software, for example a game or a screen saver, which runs in the background and displays your ad when the user enters a term related to your offer, for example a search on google for weight loss can trigger an ad about acai berry.
Banners are clickable pictures. Banners come in a lot of sizes. Most CPA offers include banners you can use to promote the offer. But successful CPA affiliates generally create their own banners, or more exactly pay someone to create banners for them.
Promoting offers in social media, for example facebook, has become popular. Note that most people using social media are not looking for something to buy, they are chatting with friends. This means that offers that require credit card details generally convert poorly on social media. But some simple CPA offers, such as an email submit, can turn out to be a winner.
Always make sure that you know the terms and conditions of the offer you are promoting. If you get caught promoting a CPA offer using methods that are not allowed, your account will most likely be terminated.
Another basic thing to do is to check for what countries a CPA offer is valid for. If you are paying for the traffic, you want to be sure that you are only paying for traffic from the countries you specify. Some offers that can be promoted world wide, will pay differently depending on in which country the customer is located. The payout for most countries may be just a tenth, or even less, of the payout for a US customer.
Some offers can be incentivized. That means you can offer your prospects something if they accept the CPA offer. Obviously, you can only try to bribe people for CPA offers that are incentive offers. For example, you could offer a free ebook about a related topic if people sign up using your link. If the offer is a simple email submit, the conversion rate can be very high. Most CPA offers can not be incentivized, so remember to check the terms and conditions of the offer.