1. Created an account on Mapbox.com
You can create a free account in seconds on Mapbox, which has a generous free tier for using their mapping technology (which is what Closeby uses to run your map).
2. Copy your Mapbox access token
You can find this by going to your Mapbox account and copying it from your Dashboard.
3. Save your access token in Closeby
Then, go to your Closeby account and save it to your account in you Map Installation page or your theme settings.
Your map will now work on your website and you'll even be able to use your own custom Mapbox themes if you want further branding options beyond what Closeby offers out-of-the-box (advanced feature). You can learn more about that here.