Question: Can anyone point me to a tutorial for electronic noobs that 
explains how to use op-amps and what I can do with them, besides
amplification?

Answer: 
Falstad [Falstad Circuit index](http://www.falstad.com/circuit/e-index.html) has an excellent Java applet that allows you to do virtual prototyping with various types of circuits.

Has a nice section on **Op amps**, whats great is the built in O'scope, volt and current meters. Right clicking on a template component in the applet brings up menu where you can experiment/substitute with different values, add remove components.
[**Op Amps for Everyone**](http://focus.ti.com/lit/an/slod006b/slod006b.pdf) (2.0 MB PDF) by Texas Instruments is a very good reference.
It covers almost any aspect you might need. Even single supply opamp techniques.