Act! Premium Desktop does not have direct Google Sheets integration. In Google Sheets, you should be able to upload any of the spreadsheets exported through the Export to Excel button, or by exporting to a CSV file.
There may be third party addons available that can integrate Act Premium Desktop and Google Sheets, but I am not aware of any.
Using the Act Premium Web API and Zapier, it would be possible to connect certain actions with Google Sheets.