How should I search for prospective businesses for affiliate marketing?

As I understand your question, you want to act as an affiliate and are looking for businesses that have programs you can tap into. (Conversely, you may mean that you are looking for affiliate partners to promote your site, but I'll focus on the first question.)

Merchants (the seller) and affiliates (sites that promote the merchants) typically come together through affiliate networks. These are clearing houses that match affiliates and merchants, provide third party tracking and may manage the payments.

There are several reputable networks, including:

Commission Junction
Pepper Jam
Directtrack

As an affiliate, you'll find tools for ranking merchants, etc.

As a merchant, these give you access to a vast range of potential affiliates.