I have a blog about coffee. How can I monetize this blog?

There are many ways but I would recommend you two different ways.
1. Affiliate marketing: Find products which could be interesting for your visitors and write reviews about them or place a banner. For example write a review about a coffee machine with an affiliate link to Amazon. Everytime someone clicks on your link and buys something you get a commission.
2. Advertising: Place ads on your blog (e.g. Google Adsense) and you get paid for every visitor. But be careful this can harm you visitors if you place too many ads!

I would recommend to start with Affiliate Marketing. Usually a good choice is to join the Amazon Affiliate program and place product links on your blog.