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 that game-breaking.
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.
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 Bonus Language.