I can't help you in regards to what happens after you leave the site to Google unless they've newer URLs we should be using the following are all we have that we can use for location lookups.
If all you provide is a location it uses the following URL to perform a location search at Google.
Code:
https://www.google.com/maps/search/LOCATION_HERE
If you provide an address you need to provide a valid address as complete as possible (zip code only likely isn't good enough) and it will use the following URL.
Code:
https://www.google.com/maps/place/ADDRESS_HERE
As for a button to get your current location it only displays if you're viewing the site with HTTPS and only if the browser gives permission to use the location API. You should see a browser notification asking for permission and if not then you've likely configured your browser to reject all requests.