The easiest and most common way to start building an audience for a website is via social media. Depending on your niche and industry, you can choose from Facebook, Twitter, Instagram, Pinterest and several other niche and location-specific networks. Building up an engaged and interested following on social media is a great opportunity to build relationships and once you have their trust, promote your products and services to them.
If you have built up an email list, you could also promote your affiliate offers via email promotions. Just make sure you build up a relationship with your audience first instead of going for the hard sell straightaway. The emails you send out must contain your affiliate links to products so when your audience click through. the sale is attributed to you.
For example, if I talk about how cool a product is, and then you find out that I’m an affiliate for them, wouldn’t you as a conscientious observer become skeptical as to whether my information is biased, if perhaps I’m only saying how cool something is because I can get paid for it? Wouldn’t that make you question my integrity with other things I say as well?