There is evidence that Wizards/Witches take an interest in literature outside of the Wizarding world.
As JKR points out in her footnotes in ToBtB:
...[This quotation demonstrates that Albus Dumbledore was not only exceptionally well-read in Wizarding terms, but also that he was familiar with the writings of Muggle poet Alexander Pope. --JKR]...
-Footnotes, The Tale of the Three Brothers, Tales of Beedle the Bard.
Given that; we see that the Magical folk do have access and exposure to Muggle writings and literature, if they so choose - this can include learner guides and so on such as http://www.dummies.com/store/Education/Language-Learning.html.
Remember, the Wizarding world is separated and kept secret from the Muggle world, but this does not mean that Wizards have zero access or exposure to the Muggle world, including its resources. Especially since most of the Wizarding community live in Muggle towns - in fact the only 'full' Wizarding town currently is Hogsmeade.
Therefore, we can assume that they learn languages and other arts the same way that they learn any Wizarding arts: by studying them.
There is also the Department of International Magical Cooperation within the Ministry of Magic.
Some of its duties include:
Assumption territory here: the Ministry has many resources, both domestic and foreign. It would be easy for them to have books and/or training or classes to learn different languages, especially in cooperation of foreign Wizards.
But it's safe to assume that they will probably need at least some understanding in other languages.
How do they learn? keep an eye out on this question: Are there spells for learning things in Potterverse?