Suggestions aren't very smart. For example, I typed "Brisbane, Australia" as the starting point and then I started to type "Mel" as the destination. Google suggested 3 places from California, strictly based on my location, while ignoring that Melbourne is a much better suggestion.
Google shows directions inside the card and you can pick between driving, walking, cycling or using public transportation.
To see the directions, just click the text that describes your favorite route. If there is only one route, pick that one. Another option is to click "directions" and go to the Google Maps site.