How to add contacts on iPhone 5s?

I just switched from iPhone 3G to 5s and I'm feeling completely stupid. Not sure why I can't figure this out…

It seems like the only way to add contacts is to import them from my e-mail contacts. I don't want to do that.

I just want to be able to manually enter a name and a phone number, but I don't see how I can do that. When I open "Contacts" it gives me the option of searching or importing them from "groups" ie the aforementioned email contacts, but there's no button for entering a new contact manually.

When I receive text messages, I select the option of "create new contact" but they still don't show up when I open my contacts. Their name only shows when I open my text messages.

Anyone know how to fix this?

Added (1). The "+" sign does not exist. That's what I'm asking about.

Bring up your contacts on your phone, hit the + sign at the top left corner, and you can manually add them.

Yes it does. If you open the Contacts app, the '+' is at the upper right part of the screen.

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