Make sure that Google Fit is either preinstalled - otherwise download it.

In order to connect Lifesum and Google Fit please click on Progress on the bottom tab bar in your Diary. On the next page click on Profile and then on the gear symbol. You will then see the option Automatic Tracking on the following page. 

Tap on Automatic Tracking.

There, you'll see a Google Fit box with a green Connect button. Tap on the button to connect to Google Fit and follow the instructions.