Analog audio is rapidly going the way of analog video, only more so. The digital revolution hit audio before it hit video, and the transition is further along. Still, you may need to deal with analog audio; here are the basics of the formats you're most likely to encounter.
¼-inch reel-to-reel is frequently used for film location audio, typically on a Nagra recorder (the standard film sound recorder, built by Nagra/Kudelski in Switzerland). Nagra audio typically runs at 7.5 inches per second (ips) or 15 ips, and it has an embedded Pilot one track, a sync reference signal at a nominal 60 Hz. Nagra playback is synced using a resolver to read the Pilotone signal and slave the Nagra's motors to 60 Hz, either using AC line frequency, a high-precision crystal oscillator, or a 60 Hz reference signal put out by the equipment the Nagra is syncing to.
There are other ¼-inch recorders for film sound, such as Stellavox and Uher machines, but they are less common. Each brand of recorder typically had its own way of recording a sync signal; check with the source of the tape if you're not sure how (or if) you should resolve a sync reference.
Other ¼-inch tapes may simply be wild sound, without a sync reference.
Nagra audio is usually full-track: the mono or stereo recording occupies the full width of the tape; when you reach the end of a reel, you rewind it for playback, just like video. Other tapes may be full-track with one or more channels, but half-track tapes are also common, where you turn the reel over once it's completed and record in the other direction. If you play back a half-track tape on a full-track recorder, you'll hear "backwards audio" from the other direction mixed with the forwards audio you expect to hear.
Multi-track audiotape is more common as a studio production format than as a field-recording format. Like multiple audio tracks on the FCP Timeline, multi-track keeps multiple channels in sync and allows for overdubbing one track while listening to another. Some multi-track tapes have a sync reference, and some even have LTC (most commonly used with a chase lock synchronizer, which listens to the timecode signal from a VTR and slaves the audio recorder to it, "chasing" the timecode), but again it's highly dependent on the recorder you use and the workflow you use with it.
Audio connections can be RCAs, phone plugs, XLRs, or even "banana plugs" on some Nagrasseparate, fat plugs for signal and ground.
Cassettes are sometimes used for location audio, mostly as wild sound. Fidelity is lower than with reel-to-reel, but the convenience and portability of cassette audio was worth the losses in sound quality.
You make cassette connections usually via RCAs, though some professional studio decks have XLRs as well.
Analog audio recorders are typically calibrated for one kind of tape: oxide, ferrichrome, metal, and so on. Some have selection switches to set the bias current and equalization for the tape type. Bias current is only used while recording; EQ needs to be properly set for both recording and playback, or frequency response will suffer.
Analog frequently employs noise reduction schemes, especially on cassette. Dolby B, Dolby C, and dbx are the most common approaches; you should label tapes with the noise reduction used so that you can use the corresponding playback setting. Using the wrong setting may result in more audible noise, frequency distortions, reduced dynamic range, and "pumping" or "breathing" artifacts from uncompensated compression.
Resolving sync on analog tapes usually means locking the recorder to line frequency during capture so that the sound doesn't drift with respect to picture. You can use a common start mark, such as a filmmaker's clapper, to align picture and sound in sync by manually aligning the sound of the clapper with the frame in which it closes.