I finally figured out how to switch default "save contact" from phone to my gmail account. (Take back up of your contacts before doing anything)
I have S3 and Note 2 with the latest android
Go to
1) settings
2) Application Manager
3) all
4) scroll down to contacts
5) Clear data
exit, exit, exit
Now go to contacts ....
Add new contact you ll get 3 options.
Select gmail ie google contact.Now when you want to add new contact it ll be stored automatically to google contact ie gmail contact.
--------------------------------------------------------------------
1. Go to Contacts, then Display Options. De-select all options except Google account (under "Choose contacts to display").

2. Enter a new contact, choose Google under "Contact Type". Save contact.

3. Re-boot Phone.
---------------------------------------------------------------------------------------

I finally figured out how to switch default "save contact" from phone to my gmail account. I have a Note2 with the latest android
Go to (I have a Galaxy S4 and instead of selecting "Phone" in the list of apps I selected "Contacts" and then cleared defaults )

1) settings
2) Application Manager
3) all
4) scroll down to Phone
5) Clear Defaults
exit, exit, exit
I rebooted... not sure if that was nessasary

now.... when I save a number from dialer or otherwise
1) add to contacts
2) Create contact
3) now I have a drop down menu (which I didn't have before... only phone) I can pick my gmail account where to save the contact
4) type in info and save
it is now in my gmail contacts
---------------------------------------------------------------------------------------