If you have an IPOD/MP3 player or you just want to download some MP3s and listen on your PC or burn them onto a CD, you can try this podcast
Arabic PodThey just go through one short conversation each episode but they really break it down and explain how to piece the sentances together and I find that listening and repeating is the best way for me to learn to speak and understand. The Arabic speaking host is Jordanian so I'm assuming some of the words/phrases he uses are from his own dialect since my husband will sometimes hear something and say "oh no, that's wrong. It should be..." but he gets the meaning so he must understand what he's saying.
Not every Arab can understand Classical or Formal Arabic. My husband warned me long ago that his mother would not understand me if I only learned to speak in fusha and I have heard a woman call into a fatwa show to ask a Saudi scholar a question and she spoke to him in her dialect and neither one of them understood what the other was saying so they had to ask another party to translate from Saudi Arabic to either Morrocan or Algerian Arabic (I can't remember which country she was from but it was one of those two) but I think most of the younger people understand Formal Arabic as well as some other dialects. My husband is Libyan and they speak a cross between Arabic and Italian there but he understands others from Tunisia (who speak Arabic/French) and Egyptians (I don't know what that dialect is a cross of) and pretty much any other dialect. He can usually tell me where someone is from just from hearing them speak in Arabic for a minute because he picks up on which dialect they are using.
If you're trying to learn to read and write then you can download and print the Madinah Books from
Fatwa Online in their download section, which can be used with this website
Madinah Arabic for free as well.
Good luck!