If you are concerned about security, the new scheme where Apple cannot see your contacts, calendars and photos, but it isn't super easy to move things. So here's a quick list for how to do it.
There are really two steps to move your contacts. First go to
google.com/contacts and export the contacts into VCF format. Then logon to
iCloud.com and go to Contacts and click on the lower left gear to do the import.
Now to actually use them properly, you need to go to each iDevice and make sure that in your contacts setting, it says you are using
iCloud for contacts and not