How to build a map with markers from single posts?

Since your blog runs on wordpress.com, your options are limited.

In order to render the map, you need the data in some form that the map can process it. Either addresses or geocodes.

In order to generate the map dynamically without manual interference, these data need to be saved with the post, and somehow retrieved.

With wordpress custom fields you should be able to save those data. This functionality is only available as VIP:

https://vip.wordpress.com/documentation/vip-development-tips-tricks/custom-fields/

Also, as far as I can see the plugin support at wordpress.com is limited.

The only thing that comes near your desire is the use of google maps, but as far as I can see I am afraid you will have to insert the markers manually. See: “embed a Custom Google Map into your WordPress.com blog”:

https://en.support.wordpress.com/google-maps/

Good luck!

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