Despite the OP specifically mentioned Dutch, the conversation has somehow steered away towards a more generic "how do I learn a language" so I'd like to add something...
These days my hometown is a very popular destination, so in case anyone plans to move to Barcelona, or anywhere in Catalonia -where Catalan is the local language- or even if you're just visiting and want to give a good impression to us Catalans, you can remotely "learn" our language thru several methods: the above mentioned RosettaStone and the like, by attending a course in one of the 150 universities around the world offering them, thru the free online course at www.parla.cat ...
And when you have managed the basics, aside from the main TV group TV3 -where you can see several of their online channels (general, news, children, sports...)- there's a very interesting program that has been working for 15 years called "Voluntariat per la Llengua" (VxL), volunteers for the language in English, where native Catalan volunteers offer their spare time to help people learning our language.
In this program, you're "matched" to a native volunteer -according to the profiles and preferences of you both- and you both commit to a 10 week 1h per week sessions to practice your language skills and to learn about our culture. These are referred to as "linguistic couples" and many of them have resulted in longterm friendships later on. Over 110,000 of these couples have been created in this period. I should clarify that "couple" refers just to two people getting together for the purpose described above :))
This is a free program -hence the reason is staffed by volunteers- and has two modalities: face-to-face and online.
The first case is aimed at those that have recently moved to Catalonia. Both you and the volunteer meet at your own convenience (ie having a stroll, a coffee, etc.) wherever you want and spend an hour talking in Catalan about whatever subjects you want, the only purpose is for you to acquire fluidity in the language and this has proven to be the best setup -rather than the formality of a classroom. As mentioned, this is to improve your communication skills, so you need to have a previous basic command of the language. The online modality is basically the same, but via Facetime, Skype or similar.
Important, for @DAV: I know for a fact that the Belgians and the Dutch, among others here in Europe, exported the experiences of this program into their own countries so this is now available also there (ie. check here for further details)
Yes, most of us native Catalans "also" speak Spanish (and English, and even some French) so you could communicate in any of these when visiting... but Catalan is the local language, so consider that. I should add that Catalan is one of the Romance languages, much like Spanish, French or Italian -among other- so for anyone having knowledge of one of them, it should be fairly easy to get to learn another one.
Enjoy!