In order to translate using the Google API key, you have to first generate an API Key in your Google account.

1. Login here: https://console.developers.google.com/cloud-resource-manager
2. Click on Menu in the left corner > APIs & services > Credentials
3. Click on Create credentials > API key
4. Check the created API Key 






In order for the API key to be active, you need to add billing details to the Google account:

1. Click on Menu left corner > Billing 
2. Click on Link a billing account or Manage billing accounts 






After these steps, you can use the Google API key in Trados Studio:

1. Open Trados Studio
2. Click on File 
3. Click on Options
4. Click on Language Pairs > Translation Memory and Automated Translation
5. Click on Use > Google Cloud Translation API...
6. Add the Google API key and click OK

*The option: Click here to obtain you API Key from Google redirects you to the Google account, in case you did not create you API Key beforehand.