My screen in Reminders is identical to what CTechie illustrated for us above.
However, when I attempt to follow instructions as per Genius76, I go to Settings / Mail, Contacts, Calendars / iCloud, and the Reminders app shows "On" already. I turned it "Off" deleted the Reminders currently saved on the iPhone. (No change in appearance of Reminders screen at that point.) Then I went back and moved the switch to "On" for Reminders once again. Then back out to Home Screen, double-click to shut-down Reminders, then re-open it, and still no "+" sign anywhere in the app. (I did successfully upgrade to iOS 5 on my iPad2, so at least I have an example of what I'm supposed to be seeing on my iPhone 3GS for Reminders.)
What I'd really like to do is uninstall/reinstall Reminders on my iPhone 3GS, but since it's not an App Store app, but a part of the iOS, I can't see how to do it? When I follow the link provided by RonAnnArbor (http://www.maclife.com/article/howtos/how_reset_ios_apps) it only seems to be pertinent to App Store apps that provide a 'black X' when you press and hold them on the home screen. Reminders does not do that?
Any suggestions?