How much amplification do you need? What's the voltage before amplification, or what's the source? If you have a line-level source (around 1V from a CD/DVD player, or a headphone output, etc.) you can use that without amplification. If you're using a microphone you'll need an amplifier with a gain of around 100 (depending on the sensitivity of the mic and how loud the sound is).
Since you're under a time-crunch, it might be best to buy an audio preamp.
The LM386 might work, but it's not an op-amp. It's a power amp, which means it's designed to drive a speaker. It's gain is adjustable between 20 and 200.
Wikipedia has basic diagrams for [u]inverting and non-inverting op-amp schematics[/u].
Since audio is AC, it really doesn't matter if you choose an inverting or non-inverting design. If you need to adjust the gain below 1 (or adjust the gain down to zero for silence) use an inverting design because non-inverting designs can't go below a gain of one. (But, you can still add a volume control to bring the signal down to zero.)
Op-amps typically run off bipolar power supplies, which means you need +12V and -12V, or +15V and -1V, etc. The LM386 runs off a single supply.
The whole concept of amplifying a voltage that varies between positive and negative really confuses me, so I don't really understand how to get it into the 0-5V range.
If you connect a battery to a speaker, you'll see the speaker move off-center (either in or out). If you reverse the battery the speaker will move in the opposite direction. Audio is AC and the current flows back-and-forth at a rate depending on the frequencies, so the speaker moves in-and-out to reproduce the sound.
Since the Arduino's analog-to-digital can't read negative voltage, and the Arduino can be damaged by negative voltage, the standard practice is to [u]bias the input[/u] at 2.5V. The two equal-value resistors make a [u]voltage divider[/u].
The 10uF capacitor "isolates" the DC bias from the amplifier while allowing the AC audio signal through and on the Arduino-side the audio signal gets added to the 2.5V bias, which means a 5V peak-to-peak signal that normally swings between +2.5V and -2.5V now swings between +5V and zero. (You can probably skip the 47nF capacitor, it filters the higher frequencies to prevent aliasing.)