This should be able via your contacts app. Hit the menu key (or tap the "hamburger icon"), go to "Import/Export", then chose to export to your SD card. This will result in a VCard file, which you also can read with other contact apps e.g. on your PC. Verify it's there, copy it to your computer for backup.
Now delete all contacts from the Google storage (e.g. via the web interface), resync, make sure they're gone. Check the settings of your contacts app again, make sure it has local storage set as its default. To be on the safe side, also go to your device's Settings › Accounts and disable contact sync.
That done, again go to the "Export/Import" menu in the contacts app, and re-import your contacts. They now should be in your local storage – and not sync'd to your Google account.
As pointed out by the OP in the comments, the original issue behind the case was Android's Contacts app (as well as several 3rd party apps) being unable to read the VCard export done on a previously used iOS device. As it often is the case, it seems some "proprietary additions" (or format mis-interpretations violating the standard) caused this. So above described procedure cured it: Android's Contacts app was perfectly capable of reading its own exports, as one should expect.