While "full" multi-tasking isn't part of the Mango experience, there are a number of developer tips to make your apps work in the background, and give the best user experience possible. These can be found scattered over various forums and MSDN posts... or gathered together by Anders Poulsen for easy reference.
As part of the Team Blog for Jayway (a software consultancy), Poulsen is running a week long series of post with hints and tips for Windows Phone developers:
The purpose of this post is to provide an overview of methods that will allow your application to seem to "run in the background" even though Windows Phone doesn't actually allow it. These methods are not hacks, they are well-documented and intended for the purpose that I describe here. I just couldn't find a good overview for this purpose anywhere else, so I decided to try to summarize the documentation from msdn.