Add contacts to group?

True. Contacts groups need to be created and maintained in the appropriate app on your computer (Address Book, on the Mac). In iTunes, on the Info tab (with the iPhone connected and selected in the devices list), you can specify a group to which new contacts created on the iPhone are assigned, but that doesn't take effect until the new, phone-created contact is synced to the computer.

I have found that if you are in "All Contacts" when you create a new contact that you do not get the option to add that contact to a group. If you first choose the group in which you want to a new contact to be in and then add a new contact, the contact will be part of that group.

For example if you have a group titled "Family", choose "Family" from the "Groups" menu (upper left hand corner after tapping into contacts) then tap the "+" button and the contact you create will be in the "Family" group.