I found it easier to use a computer logged into Gmail to input my Contacts. It was a pain, but once done ONCE, you can then use the MENU option while in your Dialer to have it display only Google contacts and to create new Contacts to Gmail. I also had to manually delete each contact that was on my SIM, which is where the problem comes from.
Basically, the non-android (dumn phone) way was to save it on your SIM. This ends up in duplicates on your phone, unless you delete everything from the SIM and get everything into Gmail. Once you do it the one time, then it is available in Gmail to be exported, if needed, and you never have to worry about backing them up.
MENU-ACCOUNTS-GMAIL accoint and make sure it is syncing contacts. Then from a computer, login to Gmail and see how ugly it is. Manually fix them in Gmail from a PC. Once done, do into the dialer on your phone and use the MENU there to show only SIM contacts, and delete them one at a time. Yes it sucks. Once all the SIM contacts are gone, hit the MENU in the dialer again, and switch it to show only Google contacts. You should be set.
Please be sure that your Gmail contacts are pristine before you go deleting the ones on your SIM. I will not feel bad if you yell at me later

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