Andrew,
The NE5532 is an old staple in the audio trade. Much of our music from the 70's 80's etc was mixed on that op amp or similar ones. It isn't up to the standard head-fiers appreciate today.
Having a bipolar input means that bias currents
must be taken into account.
Here are two links to get you started in your understanding.
Working with Cranky Op-Amps
Op Amp Bias Currents
The book that made it crystal clear to me (after re-reading it a couple times - haha) is "Electronic Circuit Guidebook Vol 3 - Op Amps, by Joseph Carr Jr, Prompt Publications, ISBN 0-7906-1131-7.
It cost me about $30 here in Canada at Active Electronics a few years ago, a company related to Future Electronics. It's not up to date re the current breed of op amps we like, but the basics are all there and I found the circuits to bring the understanding are well done.
If you still struggle, keep asking, and I'm sure other head-fiers will steer you to other resources.
You have two choices - experiment (struggle along) till you understand, or switch to jfet input op amps.
For me, playing with circuits on breadboards made all the difference. There are limits to what breadboards will do with your circuit, though.
Also, to find resources here re buffering and such, try searching on "stacked", stacking, stack. It's what they call it when they piggyback opamps or buffers to gain more current (and drop distortion). A double bonus.
Hope that helps.