1. Install the Google Maps plugin
2. Get your Google Maps shortcode
After installing and activating the plugin, you will find, in the black admin sidebar a tab called Maps. All Google Maps now require an API key to function, so get yourself your API key (you can follow the instructions available).
In the Settings menu choose all the options you want for your map. Then move to the Maps tab, where you will find your map(s) listed, with a visible shortcode. You can edit your map by clicking onto its name on the list.
3. Add the Google Maps shortcode to your Contact page
Now that you have the shortcode for your map, remaining in your WP Admin page, head over to the Appearance => Customize => Template Settings => Contact Page Settings and paste your shortcode in the dedicated field (see images below).
Now Save and Publish.