Open the Contacts app on your device
Sign in to your Google account if prompted
Tap the contact you want to save
Tap Edit
Choose the Google account as the save location
Enter or update the contact details
Tap Save
If adding a new contact, tap Add contact
Select your Google account before entering details
Fill in the contact information
Tap Save
To move an existing contact, open the contact
Tap Edit
Change the storage location to your Google account
Save the contact
Make sure contact sync is turned on in your Google account settings