Thieves' Cant isn't a written language, thus there would be nothing to understand via a spell.
Nowhere in the quote you've pulled (or the PHB) is thieves' cant ever described as a written language. This is because thieves' cant is both verbal and physical communication. Some word substitution (1 to 1) is used, but it is largely based on metaphor and contextual meaning and a big part of this is the hand symbols used when speaking. D&D's basis for thieves' cant is both historical and a trope.
The symbols mentioned are more like pictographic signs than words.
As such they are not translated, but identified, similar to how we use symbols such as the biohazard sign and nuclear sign to signify specific danger or how the symbols on a crosswalk signify when to wait and when to go. The closest living example of this I can highlight would be Hobo symbols that survive and are still in use today in the US. Different symbols would mean different things to different groups and insider knowledge for understanding thieves' cant symbols would be a must.
A 3.5 perspective - the background section of Druid in Player's Handbook:
Though their organization is invisible to most outsiders, who consider druids to be loners, druids are actually part of a society that spans the land, ignoring political borders. A prospective druid is inducted into this society through secret rituals, including tests that not all survive. Only after achieving some level of competence is the druid allowed to strike out on her own.
All druids are nominally members of this druidic society, though
some individuals are so isolated that they have never seen any highranking
members of the society or participated in druidic
gatherings.
Player's Handbook 2 gives another bit of detail:
Your secret instruction occurred in caves and forests sacred
to life. You learned clandestine verses, the names of stars
and constellations, the cycle of the seasons, sacred songs,
formulas for prayers and incantations, rules of divination
and magic, and the language of animals.
One more clue, and possibly the biggest one, is the druidic language (which remains in Pathfinder with similar restrictions). No druid can teach it to non-druids, yet all druids know it. While I cannot comment on whether this druidic society exists in Pathfinder, at least the language part must be taught by another druid. Though, generally, I'd guess a druid is similarly trained by other druids. Keep in mind this is all subject to change according to the DM's views of the setting.
As to becoming one in the game, mechanics-wise, there shouldn't be any restrictions, so long as you meet the alignment requirements. One would assume that you found a druid and got inducted into the society "off the screen". It should not be hard to pass any tests when you have character levels, and the society would be happy to have a competent and resourceful member. It is probably similar for quite a few of the classes. After all, if you multiclass as a wizard, you probably did not just buy a blank spellbook and reinvent magic?
The main consideration here is probably the convenience and enjoyment of other players - this is most likely a solo adventure, and everyone else would be just twiddling their thumbs bored.
The distinction between drawing power and being granted power is very blurry, opinion based, and subject to DM's and everyone else's interpretation of deities and the divine. Additionally, 3.5 similarly allows clerics to be dedicated to a cause, alignment or idea (and glosses over on how the non-deity clerics come to be), just as druids can be dedicated to nature, which may imply the existence of some differences.
With that out of the way, I would doubt clerics are "granted" power, except in the interpretation where gods appear to you personally or operate call centers. It's probably more a matter of establishing a divine connection, and then drawing/calling on that connection to grant you power/miracles. Which would be rather similar to druids and their connection to nature. I'd guess the "rewarded for their devotion" quote should be interpreted less directly - nobody specifically rewarded you with the power, the consequence of the process of devoting yourself to nature is access to the power of nature. The druid class then provides the combination of a connection to nature and knowledge on how to channel the power of that connection.
Best Answer
Plot: Learn it from someone who knows it
One would presume that should a druid decide to teach you Druidic, then you could spend a skill rank or two on Speak Languages to learn the language. That would be a DM’s call and probably quite rare, but it could happen. A blighter (Complete Divine) certainly wouldn’t care about teaching the language, for example.
Mind reading, memory access, or simple eavesdropping on a druid teaching a new druid may also suffice to be allowed to use Speak Language to learn Druidic. Note that the druid may lose his class features even if you force or trick him into teaching you though.
And of course, if one can find a nondruid who knows the language, that person would have no reason to refuse to teach you.
Magic: Speak all the languages
There are magical means to understand languages; comprehend languages and tongues would give one the ability to temporarily understand and speak Druidic.
A crystal mask of languages would also be capable of doing the trick. Oddly enough, while the crystal mask of languages requires that the crafter speak five languages, and then grants knowledge of five languages, nothing says they have to be the same five. Thus a psion who knows several languages could craft one that grants knowledge of Druidic.
Note that none of these actually teach you the language; they all last only as long as the spell does, or as long as you wear the item.
Epic: Polyglot feat
The [Epic] feat Polyglot says you know all languages, so that includes Druidic. Language barriers are probably not your greatest concern at level 21, though. I suppose some Dragon abuse could get you the feat earlier, which in this case wouldn’t even be game-breaking.
Prestige: Loremaster or Race: Tibbit
This is the most useful one: the loremaster prestige class gives bonus languages at 4th and 8th level. This class feature simply states that the loremaster can choose “any new language”—it doesn’t exclude Druidic like racial bonus languages do, nor does it invoke the Speak Languages skill.
Likewise, the tibbit race from Dragon Compendium includes “Bonus Languages: Any. Tibbits travel far and wide and their curiosity pushes them to learn a number of languages,” in contrast to the human entry of “Bonus Languages: Any (other than secret languages, such as Druidic). See the Speak Language skill.” Again, no prohibition on secret languages, no reference to the Speak Language skill.
Either of these could be oversights and errors, but neither has been corrected (and both books have seen errata), so I for one am willing to take them at their word.
And while Druidic itself does say that it is “a secret language known only to druids,” 3.5 has a very important rule known as “specific-trumps-general.” In this case, I would argue, the general rule is that only druids known Druidic. After all, they get it free and everyone else has to work quite hard to get it. But clearly it is possible to learn the language in general (see previous points), so the statement that only druids know it is not absolute. Polyglot specifically supersedes it. So, I would argue, does the loremaster’s or tibbit’s bonus languages. However, this is only a case I am making: you could argue the reverse, that the Druidic rules are the more specific. You will have to discuss it with your DM.