I am displaying a Google Map on a new page. How do I show the user position on the map?

Certainly I am not the first to try this. I have a new page, and on the page is a GoogleMap widget which displays a Google Map ok. The map is always centered around the capital of Barbados of all places. I want to change that so the map is centered around the physical location of the user!

How do I start doing this? Also, how do I center the map around the position of the user? And how do I test this feature in FlutterFlow which runs on my desktop development PC?

Any help is greatly appreciated!