I would like to learn Yiddish in order to further my understanding of Chassidus and other Torah topics that are presented in Yiddish. What are your suggestions for sources to use that would focus on the type of Yiddish I would expect to find in those places? Books, online and interactive programs are all helpful.
You might start with yiddishpop.com.
If you want to learn the Lubavitcher Rebbe's sichos in Yiddish, a program that presupposes very little Yiddish knowledge is Back 2 Basics Sichos. Some of the content seems to be available for free here.
There is a Yiddish translation of the Chumash written in very clear, everyday (not lomdish) language by Yehoyesh (Yehoash). A free version is here: http://yiddish.haifa.ac.il/texts/yehoyesh/tanList.htm. There is also an app here that lets you interact with the text and look up words.
I can't recommend a Yiddish textbook for beginners, except to say that Weinreich's College Yiddish is considered the standard beginners' text, and Chaim Werdyger's Yiddish in 10 Lessons looks quite good to me. Thereafter, I would recommend using Sheva Zucker's textbooks for intermediates, and finally Mordkhe Shaechter's Yiddish II for advanced students.
Once you can speak competently, you might be interested in attending the Yiddish Vokh, in Copake, NY, for practice. (It's one week at the end of the summer.)
As for learning formally: I can't give you great advice on how to learn Yiddish for religious purposes, except to say that a lot of yeshivas produce musmachim who can speak Yiddish and use it religiously. Also, Yiddish Farm (mentioned below) occasionally offers programs with a religious-Yiddish focus.
If you are serious about learning standard spoken and written Yiddish for general purposes, there are a lot of programs around the world in which to do so. The Workmen's Circle as well as significant numbers of universities provide Yiddish classes year-round. The Yiddish Farm in Goshen, NY offers live-in programs from a weekend to a year in length. There are Yiddish summer programs in New York, Israel, France, and Lithuania, among others. A very good summer program in New York is offered at the YIVO Institute for Jewish Research.
Well, seeing that no-one else has answered so far... I don't know about Hassidic Yiddish specifically but the standard textbook for learning Yiddish is Weinreich's "College Yiddish".
I'm sure there are many helpful resources online; I would start with YIVO and WikiBooks. Once you've got some basics and you want to practice, you can check out Der Forvetz, and even Hasidic Yiddish Twitter and Facebook! There's another list of more online Yiddish gathering places here.
Hope this helps! Zei gezunt and zol zayn mit mazl!
Try and learn a new word everyday-use it in a sentence.
For the Lubavitcher Rebbe's Sichos, they have a booklet of Yiddish-Hebrew translations. It's called the LSD. Likutei Sichot Dictionary.
They might have it at that place on Rehov Yishayahu, I forget the name.