1. If some change happens at one of your competitor's product (got acquired, changed a beloved feature, etc.), go through threads on public forums discussing it. You'll find a lot of current users (ie customers to poach) of that product. A recent example: Atlassian acquiring Trello.
1b. Also, look through the comment sections of news sites that reported this change. You'll also find tons of current users there.
2. Go on user submitted product review sites. Lots of them out there for different types of products: Chrome extension review page, Capterra, G2 Crowd, etc. Approach the users who left reviews expressing dissatisfaction with the competitor product. Or users who use a complimentary product.
3. If a competitor product hosts customer sites on their servers (Shopify, etc.), you can reverse lookup their IP to find all of them.
Then it's a matter of introducing your product with a semi-personalized cold email, reassuring the prospect you have the competitor product's most vital features and you also do XYZ better than them. Here's a template: http://www.artofemails.com/cold-emails#competitor
Though obviously be careful to filter those. There are some customers who are never happy with just one moon-ona-stick, who you would rather leave for your competitors to waste time on!