How to build an email list using FB Ads?

I wouldn't go ad to fan page to landing page. Inviting cold traffic to like your fan page is like sending a friend request to a stranger. Even if they accept, they're not very likely to engage with you in the future, as they don't know you!

You could direct cold traffic straight to a landing page and capture their emails that way. This works if you know exactly who your target audience are and can get your ads super narrow in the targeting. You also need a good offer (something instantly consumable like a cheat sheet, quick start guide etc) and a good quality landing page (benefit driven bullet points, CTA above the fold, consistent with ad on FB)

My preferred method is send cold traffic to ungated content such as a blog post. You'll get more people click through if they know they don't have to submit an email address to get your content. Add the Facebook Pixel to your website so that you can build a custom audience to retarget later. Add a pop up or link to your blog post inviting people to join your list. When people do join your list, send them to a thank you page and with an offer to a low ticket item (between $7-$47). This will help you make back some of the money spent on the ads.

Set up an ad targeting people who visited your website offering your opt in offer again. They're much more likely to opt in (which means cheaper conversions) once they've already seen the offer, know who you are and what you teach.