The best way to find suitable brands to promote is by simply using a search engine using: '[Brand] + Affiliate Program'. Some companies run in-house affiliate programs however, this is a very specialist area. Therefore, most companies opt to employ an 'affiliate network' which has already built a large base of affiliates and gained years of experience in running successful programs for clients.
When promoting affiliate offers, just make sure you are fully aware of all the terms and conditions attached to your affiliate program. Some programs can be strict about how they allow you to promote their products. For example, some may limit you to banner ads and links only, while others will allow you to use paid advertising, but won't allow email marketing.
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.