As these results are super-localized, the main idea is to optimize the pages you intend to rank for a specific location - make sure to add NAP (it should correspond to your actual business location though), optimize the content for a location, make the most out of your Google My Business and try gaining good Google reviews - some say they affect the maps ranking chances noticeably.

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Pretty interesting. I would guess the reviews and authority of the domain would be the main ranking factors? And obviously an optimised company description

Here are some tips to get ranking higher in Google Maps.
1. Verify your Google My Business Information
2. Get Google Reviews
3. Properly Categorize Your Business
4. Embed a Google Map on Your Website
5. Optimize the Listing Description
6. Use a Local Telephone Number
7. Add Photos to the Listing

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It's not magic. Just a bit of research and common sense. One of the best free resources explaining maps ranking can be found here.

https://cheekymonkeymedia.ca/blog/ho...le-maps-3-pack

It literally tells you everything you need to know and do.

If you want to put some money into your efforts you could look at Moz Local Services https://moz.com/local/pricingLocal.

I would say, you should choose proper category and then start asking your customer to write a review from their location and do regular activities on your Linked Google+ page.

Submit your business to google my business.

Google will send a confirmation letter to your business address.

Once you have everything in the system. Find the link to the review page of your business listing and send customers that link to leave reviews.