On page 2-9 of the ARRL Ham Radio License Manual, it discusses how in SSB one of the side bands and the carrier are suppressed to conserve power and bandwidth. Given the explanation of how AM works, however, it seems like a receiver would need the carrier in order to determine the various frequencies in the SSB; it would need the offset distance from the carrier to understand what frequency the rightmost or leftmost sidebands represent. Are SSB receivers just guessing, looking for the cluster of sidebands and assuming the leftmost is some low phone frequency?
No, the receiver does not try to determine a carrier frequency, you do. When receiving SSB, you must adjust the VFO (main frequency control), not just until you hear a signal, but also to adjust to match the suppressed carrier frequency by ear.
Slightly-off SSB signals have a distinct sound, which is not just being too low or high in pitch, because the human voice contains harmonics. For some fundamental audio frequency $f$ you have $f, 2f, 3f, …$ in some proportions, but if the VFO is offset by some amount $\delta$, the demodulated audio will have $f + \delta, 2f + \delta, 3f + \delta, …$ which do not make up the same wave shape and therefore sound funny.
In principle a receiver could attempt to automatically tune in the way you describe, but this would only work at high signal-to-noise ratios (strong signals). Doing it manually takes advantage of your human skill at recognizing human speech.
You'll quickly understand this for yourself once you have a receiver in your hands — and learn why people care about the feel of the VFO knob.
Like Kevin already wrote, the receiver doesn't "auto-tune" in SSB. In fact, I think the only modes in which there is an appreciable amount of "auto-tuning" or allowance for being significantly off frequency is modes where the absolute transmission frequency offset does not carry any important information; in other words, frequency and phase modulated modes. In amplitude modulation modes, both the absolute offset and the amplitude carries information, and what business does the receiver have deciding what I am listening to?
That said; look at a diagram of a SSB (or CW; for our purposes here, they are the same) receiver. (I'm not familiar with the ARRL material, but I would be very surprised if it doesn't have some.) You will see that the VFO setting (either directly or through some other stage, sometimes separately handled) affects the beat frequency oscillator or BFO.
Very basically, the purpose of the BFO is to "re-inject" the carrier that was suppressed in the transmitter. This then allows for easy demodulation of the RF (at this point often IF) signal. If this re-injected carrier is at the wrong frequency relative to the station you want to listen to, then the audio will become distorted.
In CW, modern receivers usually offers some means of controlling the (receiver) BFO separate from the (transmitter) tuning VFO. This allows you to change the pitch of the CW signal -- not everyone likes their CW at 700 Hz sharp. This can be termed "beat offset", "CW pitch" or something similar, but what it really does is affect the frequency difference (offset) between the indicated VFO frequency and the internal BFO frequency. In the good old days of separate transmitters and receivers, it depended on whether the two shared a VFO; if they had separate VFOs, you just tuned them slightly differently and hoped for the best; if they shared a VFO, you basically had a transceiver occupying multiple boxes in your shack.
In practice, this means that for a SSB signal to sound right, your receiver's BFO frequency needs to be very close to the (suppressed) carrier frequency of the transmitter. (This is most often achieved by simply setting your VFO such that the frequency readout is the same as that on the transmitter, assuming both are frequency-accurate; in real life, you tune until the audio sounds right.) If your BFO is off by more than a few tens of hertz at most compared to the suppressed carrier, then the signal will start to sound funny or even garbled; the audio will start to sound somewhat like Donald Duck.
Sharp filters can make this effect even more pronounced, when a part of the intended signal falls outside the main passband of the receiver's filter (which is often approximately 300-2700 Hz at -6 dB in SSB).
Tuning a SSB signal accurately will quickly become second nature once you start listening, and absent split/IF shift/beat offset/etc. you will only need to worry about tuning the VFO until the signal sounds right and then you will be right on the other station's transmission frequency. The exact frequency readout at that point is basically unimportant. (Obviously, as long as you stay within the limits of your transmission license and ultimately ensure that your entire transmitted signal fits within the band limits.)
$\begingroup$ I think it's important to keep in mind that the existence of a BFO is not fundamental to SSB. Your receiver does frequency translation from RF carrier to baseband, and the number of stages it does that in is essential neither to the modulation nor to the user interface. (I suppose given that “IF Shift”, misaligning to change filter response, is a feature, it's slightly relevant.) For example, software defined receivers have no need for a BFO. They may have a CW BFO setting, but there's no reason for it to be anything but using a different VFO-frequency for transmit and receive. $\endgroup$– Kevin Reid AG6YO ♦Jan 6, 2016 at 20:19